Preheat convection oven to 275 degrees F.
Cover a sheet pan with a silpat mat or parchment paper. Using a Japanese mandoline, julienne the apple into thin sticks, like potato sticks. Make little nests or haystacks of the sticks on the silpat, about 3 inches in diameter.
Spatter the haystacks with melted clarified butter and douse with powdered sugar from a shaker. Bake in a convection oven until dry and crisp, about 60 to 75 minutes. Or use a fruit dehydrator to dry them out. Store them in an airtight container until ready to serve.
To make the sauce, place the cider in a small saucepan, and bring it to a simmer. Continue cooking until it becomes a thick golden syrup, about 1 hour. Let cool until ready to serve. You can refrigerate it if made the day before.
To serve the dessert, place one apple hash on a dessert plate, top it with a scoop of ice cream, then carefully place another piece of hash on top as a lid. Press down gently. Spoon a "swoosh" of cider reduction on the plate and sprinkle the whole thing with powdered sugar.
Put a large mixing bowl in the freezer to chill.
In a saucepan over medium heat, bring the half-and-half, cream, vanilla bean, and star anise to a simmer, stirring occasionally to make sure the mixture doesn?t burn or stick to the bottom of the pan.
In a bowl, whisk together the egg yolks and sugar. When the cream mixture reaches a fast simmer turn it off, do not let it boil!
In a thin stream, whisk half of it into the egg yolk mixture. Then pour the egg-cream mixture into the saucepan containing the rest of the cream mixture. Cook over medium heat, stirring constantly with a wooden spoon. At 160 degrees F, the mixture will give off a puff of steam. When the mixture reaches 180 degrees, it will be thickened and creamy, like eggnog. If you don?t have a thermometer, test it by dipping a wooden spoon into the mixture. Run your finger down the back of the spoon. If the stripe remains clear, the mixture is ready, if the edges blur, it is not quite thick enough yet. When it is ready, quickly remove from the heat.
Meanwhile, remove the bowl from the freezer, put 4 handfuls of ice cubes in the bottom, and add cold water to cover. Rest a smaller bowl in the ice water.
Strain the cream mixture through a fine sieve to remove the vanilla bean pieces and star anise, into a smaller bowl. Stir in the homemade applesauce and chill 3 hours, then freeze according to the directions for your ice cream maker.
Recipe courtesy Gale Gand, "American Brasserie? by Gale Gand, Rick Tramonto, Julia Moskin, MacMillian, Publishers, 1997