When Susan Feaster was asked to host a “one-time-only” celebrity golf tournament in Monaco backed by Prince Albert II to pave the way for the 2018 Ryder Cup in Paris, she had little idea what would become of it.

Gliding around St Moritz’s spectacular Badrutt’s Palace Hotel, the white-haired Virginian, now the annual event’s president, tells me that since the first in 2016, the tournement has attracted dozens of celebrities and raised many hundreds of thousands of dollars for the Ryder Cup European Development Trust and Prince Albert’s own foundation, largely in support of grass roots and disability golf.

We’re in St Moritz, because in the alternate years, the event switches away from Monaco and to the bougie Swiss mountain resort, where a seven-storey mansion was listed for $185 million. At both, the brief is to pit celebrities and wealthy paying punters from Europe and the USA against one another in a two-day Ryder Cup-style match. Next year, the event is branching out and heading to Scotland’s Gleneagles, where the real Europe won the 2014 Ryder Cup.

‘The event took on a life of its own,’ says Feaster wryly, eight years after she organised the first. ‘Our ambition is to give our players a very unique golf experience, to develop a bond between Americans and Europeans through the sport of golf and to give back to charity.’

I’ve been invited to play in this year’s event, the grandly titled St Moritz Celebrity Golf Cup, held at Engadin Golf Club in the neighbouring Alpine town of Samedan, and – mercy of mercies – fill a spot on Team Europe, assembled to take down the Americans.

Teeing off is an unfathomable cast: there are retired American footballers – one of whom tells me he’s already regretting opening a chain of smoothie bars – a former England cricketer, a star of the Harry Potter films, a giant former Swiss international goalkeeper, several hulking long-drive specialists who strut about the place in novelty golf shirts like wrestlers with golf clubs, a host of wealthy businessmen and women and their families, and… me. Most of the paid-up team members seem to split their time between Monaco, Mexico and St Moritz.

Europe’s team captains are the former Scottish rugby internationals Max and Thom Evans, the latter flanked by his fiancée Nicole Scherzinger, who lends proceedings some genuine A-list stardust. On day one, I’m paired with Brian McFadden, once of Westlife. The genial Irishman is a regular on the celebrity golf circuit but a debutant here and seems happy to bring a sprinkling of boyish ’90s pop culture to proceedings. McFadden and I are quite the team. We win our match with two holes to spare. One point for Team Europe.

Over the two rounds, I’m pitched against some of my fellow non-celebs, who have splurged as much as 24,000 Swiss francs for their experience. One builds superyacht harbours; another is the wife of an oil and gas magnate. Another has made a fortune in bio-decontamination.

Some are event regulars, invited back for, as Feaster puts it, ‘bringing something good’, by which I come to learn she means energy – rather than just large-scale donations. This is an intimate but noisy affair, a sort of secret golfing bromocracy, where the fraternising over a cigar at the 19th hole while a DJ pumps up the volume is taken more seriously than the golf itself. Europe are behind after day one but run out winners, aided perhaps by my two points but more likely by American jet lag, and the trophy is presented at a gala dinner held in Badrutt’s Palace’s ballroom. An auction on the night adds to the charity pot.

Between rounds, while the celebrities head off to generate balcony content, I’m given a tour of the palace by Alexander Marakovits, the hotel’s PR manager who once worked for the Austrian government. He explains that the hotel has just reopened for the summer season, pulling off the dust sheets a few days early to host our event. That Feaster and her backers can convince one of “The World’s 50 Best Hotels” to open ahead of time is a sign of their clout.

Built by Caspar Badrutt in the late 19th century in the European chateau style, the labyrinthine hotel retains much of its granite charm, imperious and aloof (it’s a three-hour drive to Zurich or Milan airports) and yet cosy, like an MOD members’ club hidden behind an unmarked front door. Except Badrutt’s is unmissable. With its pinnacled tower penthouse – nightly rates up to 40,000 Swiss francs in high season – and a 1968 Rolls Royce that once belonged to the British royal family parked outside, it makes no attempt to blend into the precipitous slope behind it.

Brigitte Bardot, Andy Warhol, The Beatles and who knows who else has stayed here over the decades. Alfred Hitchcock is said to have visited more than 30 times, always staying in the same room, a lake-view suite with its own butler service that’s now named after him.‘This place is insane,’ one wide-eyed American golf influencer gushes at breakfast, as our à la carte orders are brought to us while a harpist plays.‘Our guests like it,’ says Marakovits of the harp, a refrain he offers whether describing the cellar’s 30,000 bottles of wine or the on-demand midnight access guests get to the luxury boutiques in the Badrutt’s Palace Gallery mall. He points out the new Serlas Wing over the road from the hotel entrance, an extension designed by Italian architect Antonio Citterio that will offer 25 suites with Loro Piana interiors from December.

On paper, the golfing jamboree back at Badrutt’s Palace in two years’ time is open to applicants, as next year’s Gleneagles event will be, too. But as Feaster says coyly, while “nominations are welcome”, it’s an invitation-only event. Meanwhile, for those who don’t make the list, summer mountain golf at Badrutt’s Palace will only ever be a click away. And that’s worth the trip alone.

stmoritzcelebritycup.com; badruttspalace.com