Rosé-poached pear tart with chai custard

1. For the custard, in a small saucepan, bring the milk, and chai to a simmer over medium-high heat. Remove from heat. Cover and let steep until the milk is infused, about 30 minutes. 2. In a medium saucepan, whisk the sugar, cornstarch, and 1/4 tsp. salt. Whisk in the egg yolks, then 1/2 cup of the hot milk. Gradually whisk in the remaining hot milk. Cook over medium-high heat, whisking constantly, until the mixture begins to boil and thicken, about 5 minutes. Continue boiling and whisking for 1 minute more. Strain into a medium bowl. Add the butter and vanilla. Whisk gently until the butter melts. Press a sheet of plastic wrap directly on the surface of the custard to prevent a skin from forming. Refrigerate until cold, at least 4 hours or overnight. 3. In a large skillet, bring the wine and 2/3 cup sugar to a boil, stirring until the sugar dissolves. Stir in the vanilla. Add the pears. Reduce heat to medium. Simmer until the pears are tender, 10 to 20 minutes (depending on the firmness of the pears). Strain the pears over a medium bowl. Pour the syrup back into the skillet. Boil the syrup until reduced to 1/2 cup, about 15 minutes. Return the pears to the syrup. Cover and refrigerate until the pears turn pink, at least 4 hours or overnight. 4. For the crust, in a food processor, pulse 1 cup all-purpose flour, the hazelnut flour, the remaining 3 tbsp. sugar, and 1/2 tsp. salt. Add the butter and pulse until the dough resembles breadcrumbs. Add the egg yolk and pulse until the dough comes together in a ball. Lightly spray a 9-inch tart pan with a removable bottom with cooking spray. Press the dough onto the bottom and up the sides of the pan. Using a flat-bottom drinking glass or a metal measuring cup, press down on the crust until it’s even and smooth. Freeze the crust until firm, about 30 minutes. 5. Preheat the oven to 190° C. Line the crust with foil and fill with pie weights or dried beans. Bake for 20 minutes. Remove the foil and weights. Using a fork, pierce the bottom of the crust all over. Bake until golden brown, about 20 minutes more. (Pierce the crust with a fork if it puffs up.) Let the crust cool. 6. Strain the pears over a large skillet. Boil the syrup over medium-high heat, stirring occasionally, until thickened and reduced to about 3 tbsp., about 10 minutes. Fill the crust with the custard. Top with the pears. Just before serving, drizzle with the syrup. Make it Ahead: The crust, custard, and poached pears can be made a day ahead. Wrap the baked crust in plastic or foil and store at room temperature. Keep the pears and custard covered and refrigerated. The tart can be assembled up to an hour before serving.