There's a recipe for a gallon of a similar ice cream in my old Farm Journal canning cookbook from the 60's-it sounded wonderful, save for the raw, whole eggs.
I made a few changes (reduced the quantity, cooked a custard base, toasted the coconut) and the results were delicious. This is the sort of ice cream I cannot make too often as I doubt I'd be able to practise good self control around it. I don't really know how I'll sleep tonight knowing I have a pint in the freezer. Like Sirens, they are, those pints of homemade ice cream calling to me from the freezer. Small batches are good-less damage in a worst case scenario.
You Will Need:
1/2 cup honey
2 tablespoons granulated sugar
3 large egg yolks
1 cup heavy cream
1 cup whole milk
1/4 teaspoon allspice
1 teaspoon coconut extract
1 teaspoon vanilla extract
1/2 cup crushed pineapple, well drained (it wouldn't hurt to squeeze it dry)
1/2 cup toasted coconut
In a heat-proof bowl, whisk the yolks and granulated sugar together until light. In a saucepan, heat the cream, milk, and allspice until steaming. Carefully whisk the milk into the egg mixture in a thin stream taking care not to cook the eggs. If you suck at this sort of thing (don't worry, that isn't some sort of character flaw) go ahead and temper the egg mixture properly. I do use a strainer at the end to catch any bits of cooked egg, but do whatever works best for you. Return the mixture to the pan and cook until it reaches 170 degrees f. or coats the back of a wooden spoon (if you run a finger through it and it leaves a clean line, the custard is done).
Strain into a heatproof bowl. Whisk in the honey, extracts, and if desired, a pinch of salt (I do this, but I don't know that it really makes any difference-habit I suppose). Pour into a metal pan (glass is OK too) and place in freezer 30 minutes. With a fork, scrape around the perimeter, and mix well. return to freezer. Continue doing this until ice cream is mostly firm. If you should forget it, and it freezes solid, no harm done-simply scrape it into a bowl and give it a quick blitz with a hand mixer. When the ice cream is mostly firm, but still workable, stir in the fruit and coconut (I suppose coconut is a fruit then?). Transfer to a freezer container and chill several hours until firm.