Recipe - Pear and Chocolate Cake Tart

This is a really beautiful and impressive tart, and it is also very delicious. The dessert is both decadent, with the dark chocolate and dense pastry crust, and light, with the poached pears. The chocolate has the consistency of a cake, hence the name. This recipe is adapted from Clotilde Dusoulier's book Clotilde's Edible Adventures in Paris.

For the pastry shell:

1 large yolk, saving the white for later
3 tbsp and 1 tsp ice water
2 tbsp sugar
2 cups all purpose flour
1 stick (8 tbsp) + 1 tbsp of salted butter (softened to room temperature)

For the pears:

2 tbsp sugar
1 cup water
3 tbsp dark rum
2 ripe pears (a sweeter, fragrant variety will add to the tart best - try to find juicy pears)

For the chocolate filling:

3 tbsp all purpose flour
1/4 tsp baking powder
5 ounces of quality, bitter chocolate (should be about 70% cocoa)
7 tbsp salted butter, diced
1/2 cup sugar
1 egg
1 egg white

Crust:

-Beat the egg yolk, water and sugar in a small bowl
-Using a food processor, or by hand, combine the flour and butter until they are combined into crumbs
-Add the yolk mixture and further combine, adding more ice water a teaspoon at a time, if needed
-Place dough on a floured surface, push into a ball without rolling
-Cover in plastic wrap and refrigerate for 30 minutes to 24 hours
-Remove dough, letting sit for 10 minutes if it has been in fridge over an hour
-Grease a 9" tart pan with butter
-Roll out the dough on a floured surface into an 11" circle
-Line the tart pan with the dough, crimping and trimming edges
-Cover in plastic wrap and refrigerate for 30 minutes
-Preheat oven to 350 degrees
-Remove dough, prick in several places on the bottom with a fork and bake for 10 minutes

Pears:

-Peel the pears and cut them in sixths, being sure to discard the cores
-Combine the other ingredients in a saucepan and let simmer on medium heat
-Add the pears and keep simmering until the pears have softened, about 10 minutes
-Remove the pears and set them aside to cool

Chocolate filling:

-Mix the dry ingredients in a bowl and set aside
-In a double broiler, melt the butter and chocolate over medium heat
-Remove from heat and add sugar, stirring constantly, then the eggs, and finally the dry ingredients, stirring until everything is combined
-Pour the chocolate mixture into the baked tart shell, making sure it's level
-Add the pears on top of the chocolate in a circular pattern, with the narrower tips toward the middle
-Bake at 350 degrees for 20 minutes, until the center is just firm
-Let cool before serving, with a dollop of creme fraiche or whipped cream, or on its own