Mix flour, sugar, and salt in a large bowl. Add butter; cut butter with the flour using a pastry knife, or by using your fingers, until mixture resembles coarse meal.

Add egg yolks and mix with a fork until dough beings to clump together.

Shape dough into ball; flatten into a disk.

Wrap in plastic wrap and chill for at least 30 minutes. Dough can made up to 2 days in advance. Let soften slightly at room temperature before rolling out

Roll out pastry between two sheets of parchment. Transfer to tart pan with removable bottom.

Press crust into the bottom and up the sides of the pan. Trim dough overhang to 1/2 inch; fold in and press, forming double thick sides.

Freeze crust until firm; about 30 minutes.

Pour milk into small saucepan.

Scrape in the seeds from vanilla bean; add bean.

Bring to a simmer. Remove from heat.

Whisk egg yolks, sugar, cornstarch and almond extract in a bowl to combine.

Gradually whisk milk mixture into yolk mixture. Return saucepan to heat.

Whisk over medium heat until custard thickens and boils, about 2 minutes.

Discard vanilla bean.

Transfer custard to a bowl and place plastic wrap directly onto surface of custard; cover and refrigerate until cold, about 4 hours.

Preheat oven to 350 degrees F.

Combine almond slivers and powdered sugar in a small bowl.

With a fork, blend in the butter, then the whole egg and salt.

Add this mixture to the cooled custard and mix until well combined.

Pour into cooled crust; smooth top.

Arrange apricot halves, round side up, atop the filling.

Sprinkle with slivered almonds.

Bake tart until filling is set and golden, about 45 minutes. Remove from oven.

Brush with honey or agave and return to the oven for 3 minutes.

Cool tart completely in pan. Remove from pan and transfer to a plate.