Mix flour, cold butter, and sugar until crumbly, then add egg yolk and water to form dough.
Shape into a disc, wrap, and chill for 30 minutes.
Roll dough and cut rounds to fit tartlet molds; press into molds.
Beat soft butter, sugar, egg, almond flour, and extract into smooth frangipane.
Pipe or spoon filling halfway into each pastry shell.
Nestle apricot halves into the filling.
Top with sliced almonds and bake at 350°F for 20-25 minutes until golden.
Cool slightly, then dust with powdered sugar before serving.
Tip: Keep pastry cold for the flakiest shells.
Tip: Do not overfill to prevent overflow during baking.