Preheat oven to 400°. Line a rimmed baking sheet with parchment paper.

Transfer each round to a 3¾-inch removable-bottom fluted tartlet pan. Using the wide end of a chopstick, gently press dough into indentations in sides of pans. Trim excess dough . Using a fork, prick bottom of each tartlet dough .f'times. Place tartlet pans on prepared baking sheet.

In a small bowl, lightly whisk 1 egg. Brush a thin layer of beaten egg onto tartlet dough. Top each with a sheet of parchment paper, let­ ting ends extend over edges of pans. Add pie weights.

Bake for 12 minutes. Let cool completely on ·a wire rack. Carefully remove parchment and weights. Reduce oven temperature to 375°.

In the work bowl of a food proces­ sor, pulse pecans until finely ground.

In a medium bowl, beat together butter, sugar, apple pie spice, cin­ namon, and salt with a mixer at medium-low speed until creamy. Add egg white and remaining 1 egg, beating until incorporated. Using a rubber spatula, scrape sides of bowl.

With mixer at low speed, add ground pecans, flour, and vanilla extract, beat­ ing until well combined. Divide pecan filling among prepared tartlet pans, smoothing tops with an offset spatula.

Using setting #2 on a French mandoline, thinly slice apples. Using a sharp knife, cut into ¾-inch-l ong slices. Place apples in a microwave-safe bowl, and cover with a damp paper towel. Microwave for 30 seconds so apples are easily pliable. Arrange apples on top of pecan filling in a rose pattern, peeling edges up.

Bake on bottom rack of oven for 15 minutes . Cover with foil, and bake until a wooden pick inserted in cen­ters comes out clean, approximately 15 minutes more. Let cool completely on a wire rack.

Just before serving, carefully remove tartlets from pans. In a small microwave-safe bowl, stir together apple jelly and 2 tablespoons water. Microwave on high until smooth, approximately 30 seconds . Brush onto tartlets. Serve immediately .