Preheat the Oven - Set the oven rack in the middle position. Preheat to 350°F (176°C). Line two large sheet pans with parchment paper.
Sift the Dry Ingredients - In a medium bowl, sift the all-purpose flour, almond flour, and baking soda. Add the salt and whisk to combine. Set aside.
Cream the Butter - In the stand mixer bowl fitted with the paddle attachment, add the softened butter and almond paste. Mix on medium-low speed (setting 4) for 1 minute. There may be some lumps of paste remaining.Add the granulated sugar. Mix on medium-low speed (setting 4) until the mixture is light and fluffy, about 2 minutes. Scrape the sides and bottom of the bowl with a rubber spatula.
Make the Dough - Add the egg and almond extract to the bowl. Mix on medium-low speed (setting 4) for 20 seconds. Scrape down the sides and bottom of the bowl with a spatula.Carefully add the bowl of dry ingredients to the mixing bowl. Pulse the mixer on and off about 12 times. Turn the mixer to low speed (setting 2), and mix until the dough just comes together, about 10 to 15 seconds. Stir with a spatula any dry bits on the bottom of the bowl.
Roll Out the Cookies - Create 1 tablespoon dough balls (20 grams), about 1 ¼" in size. Place them about 2" apart on the lined sheet pans, about 13 per sheet.Gently flatten the tops with the palm of your hand or the flat side of a measuring cup. Do not flatten too much, less than halfway down. Press a sliced almond on the top of each cookie.
Brush with Eggwash - In a small mixing bowl, whisk together the egg yolk and water. Brush the tops and sides of the dough ball with the egg wash.
Bake the Cookies - Bake one sheet pan at a time for 7 minutes. Rotate the pan and continue baking until lightly golden brown, about 6 to 7 minutes. Repeat the process with the remaining trays, but make sure the oven comes back up to temperature before baking.
Let Them Cool - Leave the cookies on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely.
Notes
Storing: Store unbaked cookie dough covered in the refrigerator for up to 1 day. Store baked cookies in an airtight container at room temperature for 7 days.
Omitting Almond Paste: Use 2 teaspoons of almond extract instead of ½ teaspoon when adding the eggs to the creamed butter and sugar. The nutty flavor might not be as intense and slightly crisper.