1. Make the pastry cream: Bring milk, heavy cream, vanilla seeds and pod, and 2 1/4 teaspoons granulated sugar to a gentle simmer in a medium saucepan over medium heat. Remove from heat; discard vanilla pod.

2. Meanwhile, whisk remaining 2 1/4 teaspoons granulated sugar and the cornstarch in a large bowl. Whisk in egg yolks. Gradually add one-third of the hot milk mixture, whisking constantly. Whisk in half the remaining milk mixture, then return the entire mixture to saucepan. Cook, stirring constantly with a rubber spatula, until thickened, about 2 minutes.

3. Strain pastry cream through a fine sieve into a bowl. Whisk in butter. Press plastic wrap directly onto surface to prevent a skin from forming. Let cool completely. Refrigerate until ready to use.

4. Make the poached pears: Bring granulated sugar, 3 1/2 cups water, and vanilla seeds and pod to a boil in a medium saucepan over medium heat. Add pears. Reduce heat to medium-low. Cover with a round of parchment, and cook until pears are just tender when pierced with the tip of a sharp knife, about 30 minutes. Let pears cool in syrup, about 1 hour.

5. Meanwhile, make the tart shell: Roll out puff pastry to a 10-by-11-inch rectangle on a lightly floured surface. Press an inverted 10-inch fluted tart pan into the pastry to cut out a round. Using a paring knife, score a 9-inch circle (without cutting all the way through) inside the round, making a 1-inch border. Prick inner circle all over with a fork. Brush outer edge with egg wash. Slide pastry onto a parchment-lined baking sheet, and refrigerate for at least 30 minutes.

6. Preheat oven to 400 degrees. Bake pastry until puffed and golden brown, about 20 minutes. Let cool.

7. Assemble the tart: Remove pears from syrup using a slotted spoon, and cut into 1/2-inch-thick slices. Spread pastry cream onto inner circle of tart shell. Fan pears and tangerine over top, alternating every 2 pear slices with a tangerine segment. Sprinkle with superfine sugar. Hold a small handheld kitchen torch at a 90-degree angle 3 inches from sugar topping. Move flame back and forth until sugar melts and turns golden brown. (Alternatively, heat broiler and bake pie on top rack until sugar starts to brown, about 2 minutes.)