In a mixing bowl, combine the flour and sugar. Add the softened butter and work it into the dry ingredients using your fingertips until the mixture resembles coarse crumbs. Incorporate the egg yolks and gently knead the dough until it becomes smooth. Wrap the dough in plastic wrap and refrigerate it for 30 minutes to firm up.

Cream the softened butter and sugar together until light and fluffy. Beat in the egg and almond extract, mixing thoroughly. Carefully fold in the almond flour until the filling is well combined.

Preheat the oven to 350°F (175°C). On a lightly floured surface, roll out the chilled dough to roughly ¼ inch thickness. Cut out rounds that fit your tartlet molds and gently press the dough into each mold.

Evenly distribute the frangipane filling into the prepared pastry shells. Top with sliced almonds and sprinkle a small amount of almond flour over each tartlet for added texture.

Place the tartlets in the oven and bake for 25 to 30 minutes, or until the filling is set and the crust is golden brown.

Warm the apricot jam slightly, then brush it over the baked tartlets to give them a glossy finish and a touch of sweetness.

Allow the tartlets to cool in their molds for about 10 minutes before removing. Serve them warm or at room temperature, as preferred.