There’s no point trying to work out what’s in a Killer Bee — and after you’ve had a couple you won’t care anyway. I’m talking about a now-legendary cocktail dreamed up by its equally legendary creator, Sunshine.

I’m on the tiny Caribbean island of Nevis and I’ve made tracks to Sunshine’s, a beach bar situated on Pinney’s Beach, a pristine three-mile-long sandy stretch next to the island’s charming, stuck-in-a-time-warp capital, Charlestown. Sunshine’s looks like any other humble, colourful Caribbean beach shack, except for the array of framed photos of its A-lister regulars hanging on the walls.

Most of the illustrious subjects pictured — from Oprah and John Travolta to Roger Daltrey and Beyoncé — have their arms around the man himself. But whatever incentive you try and dangle under his nose, he won’t part with his recipe for the cocktail that draws his illustrious customers in, along with a plate of his superior beach-shack nosh.

“Hey, it’s just a slightly different take on a rum punch — Antiguan rum — because that’s the best in this part of the Caribbean, combined with freshly squeezed passion fruit,” he says with a shrug and a grin. But you can bet there’s more to it than that — and he’s not sharing. I suspect the liberal use of overproof rum; you can certainly believe it when locals gleefully tell you that after two Killer Bees, you’re buzzing.

Hey, it’s just a slightly different take on a rum punch...

Sunshine’s wealthier patrons even fly him over to their homes in the Hamptons, to recreate his addictive cocktail, along with his signature dishes of garlic butter lobster and blackened snapper. The latter is particularly good and Sunshine is happy enough to share his recipe for that: blend together peeled garlic cloves, spring onions, celery, hot peppers and red bell peppers with olive oil and salt, and slather all over the fish before slapping it on a white-hot charcoal grill. That’s all there is to it, he says. He serves it with grilled vegetables and that Caribbean staple, rice and beans.

Sunshine with his addictive cocktail, the Killer Bee, whose ingredients are a closely guarded secret

Sunshine with his addictive cocktail, the Killer Bee, whose ingredients are a closely guarded secret

It goes without saying that the fish was plucked from the sea earlier that morning; Sunshine has a network of fishermen with whom he works, boasting that he can take his pick of the best. The vegetables are grown in the little kitchen garden he tends alongside the shack; others he can choose from a host of nearby growers as Nevis is a veritable Garden of Eden.

At only 36sq miles in area and with a population of 12,000, the small, verdant island state of Nevis is federated with the significantly more populated St Kitts, a 20-minute hop across the water. Sunshine was born on St Kitts, but came to Nevis in 1994 when he realised that guests at the recently opened Four Seasons Resort wanted a more relaxed alternative. So he set up his charcoal grill and beach bar and never looked back.

“Wherever visitors choose to stay, even if it’s at a five-star hotel, they still want to meet locals and experience local culture. It’s the people who make Nevis,” reasons Sunshine. He’s not wrong.

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