For the frangipane

1. Mix. In a food processor, blend together almond flour, sugar, salt, butter and egg until mixture is fairly smooth. Transfer to a storage container and chill.

For the crust

1. Mix. In a food processor, blend together flour, sugar, butter, and salt just until mixture resembles coarse crumbs with some roughly pea-size butter lumps.
2. Add water. Drizzle 3 tablespoons ice water evenly over the mixture and pulse in processor until incorporated. Squeeze a small handful together. If it doesn’t hold together, add more ice water, ½ tablespoon at a time, pulsing until just incorporated, then test again. I usually end up using 4 tablespoons of water.
3. Gather together. Gather dough together into a ball, then flatten into a ½-inch thick disk. Wrap dough in plastic and chill until firm, about 1 hour.
4. Roll out. Roll out dough into a large thin round on a lightly floured surface with a floured rolling pin. Using a bowl or plate as a guide, cut out 3 7-inch circles. It does not have to be perfect – the uneven edges give the tarts a nice rustic look. Transfer the rounds to 3 (4-1/4 inch diameter) tartlet pans with removable bottoms. Ease dough into the pans and pat firmly into the bottoms and up the sides letting any extra dough hang over the sides. Gather dough scraps and roll out another thin round large enough to cut out another 7-inch circle. Fit dough into fourth 6-inch tartlet pan.
5. Chill. Chill dough in tartlet pans until firm, about 30 minutes.

For assembling the tarts

1. Prep oven. Heat oven to 400 degrees F.
2. Prep apples. While the dough is chilling, prepare the apples. First, peel all the apples. Then cut each apple top to bottom as close to the core as possible without cutting through the core. Use a melon baller to scoop out any seeds or parts of the core. Slice each apple half into 1/4-inch slices. Keep the slices together as you cut. This makes transferring the slices to the pans easier.
3. Assemble. Remove tartlet pans from the fridge. Spread a layer of frangipane in the bottom of each tartlet (I use about 1 tablespoon per tartlet). Arrange apple slices on top of the frangipane. Fold any dough hanging over the edges of the pans back onto the apples; crimping dough as necessary.
4. Sprinkle. Brush tartlets with the melted butter and sprinkle with sugar.
5. Bake. Bake in oven for 40-50 minutes until crusts are golden brown and apples have softened. Transfer baked tartlets to a wire rack to cool.
6. Glaze (optional). If doing the apricot glaze – warm apricot jam in the microwave for 15-20 seconds (it just needs to be warm enough so that it can be brushed). Using a pastry brush, brush jam on warm tartlets.
7. Cool. Let tartlets cool before serving then serve with vanilla ice-cream, if desired.