Step 1Whisk the sugar and egg yolks together in a bowl.
Step 2In a small, heavy saucepan, bring the half-and-half and zest just to a simmer; do not boil. Gradually whisk half the hot mixture into the yolk mixture. Return to the saucepan. Cook over medium heat, stirring constantly, until the custard thickens and coats a spoon, about 5 minutes. Do not boil. Strain the custard into a clean bowl. Whisk in the tangerine juice and vanilla. Refrigerate for at least 2 hours or up to 2 days.
Step 1Butter a 9-inch round cake pan.
Step 2Stir the sugar and water in a nonstick skillet over low heat until the sugar dissolves. Increase the heat and simmer, without stirring, until the color is a deep amber, about 10 minutes, swirling the pan occasionally and brushing down the sides with a wet pastry brush. Pour the caramel into the prepared pan, tilting to coat the bottom. Overlap the pears in concentric circles on top of the caramel.
Step 1Heat the oven to 350 degrees.
Step 2Stir the flour, baking powder and salt together in a small bowl.
Step 3In a large bowl, cream the butter and sugar together until fluffy. Add the eggs and zest and beat until light and fluffy.
Step 4Combine the milk, cream and Cognac in a small bowl. Alternately add the flour mixture and the milk mixture to the butter mixture in thirds, stirring to blend after each addition. Stir in the nuts. Pour the batter over the pears.
Step 5Bake until the cake is golden and a tester inserted in the center comes out clean, about 1 hour. Let cool in the pan on a rack for 5 minutes. Run a knife around the edges, place a platter over the cake, and invert. Let rest for 1 minute, then remove the pan. Serve the cake warm, with the cold Tangerine Custard Sauce on the side.