for the shell
1-1/2" cup flour
1/4 teaspoon salt
1/3 cup sugar
3 large egg yolks
1/2 teaspoon vanilla extract
1/2 cup cold unsalted butter, diced
for the tart
6 tablespoons unsalted butter
1-1/2 large eggs
1/2 cup plus 1 tablespoon sugar
3 tablespoons all-purpose flour
4 ripe pears (Anjou or Bartlett)
2 tablespoons lemon juice
for the glaze
1/2 cup apricot jam
1 tablespoon water
1/4 cup sugar
Preparing the pastry dough
Sift the flour on a work surface and make a hole in the center. Place in the hole salt, sugar, egg yolks, vanilla and butter.
Mix the butter with the yolks and draw the flour gradually into the mix.
Work quickly with your hands, to form dough—avoid warming the dough too much. Sprinkle lightly the work surface with some flour to prevent the dough from sticking to the table.
When the dough is smooth, elastic, and consistent, form it into a ball cover with plastic wrap, and keep in the refrigerator for about 30 minutes to 1 hour.
Preparing the custard
Melt the butter and let it cool to room temperature. Place the eggs in a mixing bowl. Whisk in the sugar. Whisk in the flour. Whisk in the melted butter. Set aside.
Assembling the cake
Preheat oven to 375 F (180 C). Remove the dough from the refrigerator. Butter a shallow tart pan—10 inches (25 cm) in diameter x 3/4-inch (2 cm) deep, with a removable bottom—and sprinkle with a small amount of flour.
Using a rolling pin on a floured surface, flatten the larger portion into the shape of a disk, slightly larger than the pan.
Place the disk flat in the pan and with your fingers push it to uniformly cover the bottom and the sides of the pan. Trim the excess dough and patch the edges if necessary.
Place in a large bowl cold water and 2 tablespoons of lemon juice. Peel the pears. Cut them in half. Remove seed and core, and place into the bowl with lemon water to keep prevent darkening.
Remove the halves from the water one at the time, and dry well with a towel.
Slice the pear halves crosswise on an angle about 1/8 inch thick slices. Keep the half pear together.
Transfer the sliced half pear to the pastry lined pan, with the narrow tip toward the center. Push the slices inward to fan them slightly. Repeat this step with all the pears in a fan design.
Pour the custard filling in the empty spaces around the pears, but not on top of them. The custard should be only half way up the side of the pears.
Bake for 20 minutes at 375F (180 C). Reduce oven 350F (170 C) and bake until fully cooked an golden. if the edges of the tart start coloring too much cover the cake with a aluminum foil and finish baking. remove from the oven and let the tart cool.
Making the glaze
In a small pan over medium heat melt the apricot jam. Stir in the water to make the jam thinner. Strain the jam through a fine sieve to remove the fruit pieces.
Brush the pear halves with a thin coat of jam. Serve lukewarm.