For the Cream Cheese Dough:
In an electric mixer fitted with the paddle attachment, cream the cream cheese and butter until smooth. Add the all-purpose flour and mix until just combined. Refrigerate the dough for at least 1 hour before proceeding. On a lightly floured surface, roll out the dough to 1/8-inch thick and, using a plate as a guide, cut into a circle to fit a 10-inch springform pan. Refrigerate the cut dough for 15 minutes before forming it into the pan, doing so makes it easier to shape. Refrigerate while you make the pound cake batter.
For the Pound Cake "filling":
Preheat oven to 400 degrees F and position a rack in the bottom third of the oven.
In an electric mixer fitted with the paddle attachment, cream the butter and sugar until light and fluffy. Combine the all-purpose flour, baking soda and salt in a bowl and set aside. In a separate bowl, combine the buttermilk and vanilla extract. Add the egg and mix until combined. Add 1/3 of the flour mixture and mix until just combined. Follow with 1/3 of the buttermilk mixture. Repeat until both the flour mixture and buttermilk mixture have been used, making sure to not over mix.
Pipe the pound cake batter onto the unbaked crust in the bottom of the springform pan, making sure that the entire crust is covered in 1 even layer. Take each pear half and slice crosswise into very thin slices (the thinner the slices, the better the tart looks). Carefully fan out the pear halves onto the cake batter, arranging the stem side of the pears towards the center of the tart and the rounder pear bottoms towards the outer edge of the springform pan. Bake on the bottom shelf of the oven for about 45 minutes, or until the pound cake is light brown. The pound cake batter will rise around the pear halves. Transfer the tart to a wire rack to cool. Allow to cool for 10 to 15 minutes, then brush the tops of the pears lightly with some of the apricot jam.
When the tart is cool, cut into 6 or 8 slices and serve with a scoop of the Ginger Ale Ice Cream and a zig-zag drizzle of the Creme Anglaise.
Place the ginger ale in a large, heatproof mixing bowl and set aside.
Combine the cream, milk, vanilla seeds and bean in a medium heavy saucepan and heat until mixture almost comes to a boil. Remove from the heat.
In a heatproof mixing bowl, whisk the egg yolks and sugar until frothy and lemon colored, about 2 minutes. Whisk 1 cup of the hot cream mixture into the egg yolks in a slow, steady stream. Gradually add the egg mixture to the hot cream and return to the heat. Cook, stirring constantly, until the mixture thickens enough to coat the back of a spoon, about 5 minutes.
Remove from the heat and strain through a fine mesh strainer into the ginger ale. Stir to combine, then immediately transfer bowl to an ice bath, stirring frequently until cool. Refrigerate until well chilled, about 2 hours.
Pour mixture into an ice cream maker and freeze according to the manufacturer's instructions. Transfer to an airtight container and freeze until ready to serve.
Place the yolks and sugar in a heatproof mixing bowl and whisk until thick and lemon colored.
Heat the cream, vanilla seeds and bean in a nonreactive saucepan to the scalding point (when bubbles form around the edge of the pan). Gradually add the cream to the yolk mixture, beating constantly. Return the mixture to the saucepan and continue to cook over low heat until the mixture thickens and coats the back of a spoon. Do not overcook or boil, as the sauce will curdle. Strain through a fine-mesh sieve into a clean bowl set over an ice bath. Stir until cooled, then cover with plastic wrap, pressing it down on the surface to prevent a skin from forming, and refrigerate until thoroughly chilled.
Serve drizzled or spooned over desserts, either cold or warm.