Step 1Place one-half cup sugar with the corn syrup in a pot with just enough water, about 2 tablespoons, to wet the sugar to a wet sand consistency. With a pastry brush dipped in water, clear off the edges and sides of the pot to be sure there are no loose sugar crystals. Cook the mixture over medium-low heat until it turns a dark amber color. Pour it into the bottoms of the four ramekins and allow to cool.
Step 2Heat the oven to 500 degrees. Toast the hazelnuts until golden brown. Remove and allow to cool. When cooled, put the nuts into a food processor with one-quarter cup sugar and process until finely ground.
Step 3In a medium pot, bring the milk and cream to a boil. Add the hazelnut mixture, cover and steep for one hour off the heat.
Step 4In a large bowl, whisk the yolks, egg and remaining one-quarter cup sugar. Reheat the milk mixture to boiling. Pour the milk mixture into the egg mixture in a steady stream, whisking constantly. Strain through a chinois or cheesecloth-lined strainer.
Step 5Heat the oven to 300 degrees. Pour the mixture into the ramekins, then place the filled ramekins into a baking pan. Fill the pan with a one-inch water bath of boiling water.
Step 6Cover the pan with foil and bake for 25 minutes, or until the edges are set but the centers still jiggle. Let cool and refrigerate for at least 3 hours or overnight.
Step 1Cut the apricots in half, remove the pits, and place them skin-side down in a ceramic or glass baking dish.
Step 2Split the vanilla bean in half lengthwise and with the back of a knife, remove the seeds. Mix the seeds and bean with the sugar and sprinkle it over the apricots. Roast them uncovered at 350 degrees until they are soft and begin to caramelize, about 45 minutes.
Step 3Add the wine, which will deglaze the pan and form the sauce. Discard the vanilla bean. Reserve half the sauce and 8 apricot halves for presentation; the remainder is used for the sorbet.
Step 1Bring the sugar and water to a boil. Once the sugar is dissolved, remove it from the heat and cool (this is the simple syrup).
Step 2In a blender, place the 32 apricot halves, half of the apricot sauce from the roasted apricots and one-quarter cup simple syrup and blend until smooth, adding more simple syrup if necessary.
Step 3Freeze in an ice cream maker according to manufacturer's instructions.
Step 1Unmold the flan by running a butter knife around the edge of each ramekin and inverting the flan onto a plate. Tap the ramekin against the plate if necessary.
Step 2Slightly warm the roasted apricots with the sauce and place two warmed apricots on a plate next to the flan.
Step 3Drizzle apricots with the sauce and add a scoop of ice cream on top of the flan. Sprinkle a few hazelnuts around the flan. Serve immediately.