Make the frangipane filling. In a medium bowl, whisk the egg with a fork until broken up, then mix in the almond flour, sugar, melted butter, vanilla extract, and almond extract. Once a smooth filling forms, cover the bowl and refrigerate until ready to use.
Prepare the cookie dough. To a medium bowl, add the all-purpose flour, almond flour, baking soda, and salt and mix until combined. Set aside.
In a large bowl, stir together the melted butter, sugar, and powdered sugar until homogeneous. Whisk in the egg, egg yolk, almond extract, and vanilla extract.
Once smooth, stir in the dry ingredients until a dough forms and no dry spots remain. Do not overmix.
Line a baking sheet with wax or parchment paper and set aside. Using a 1 to 1.5 ounce scoop, portion the cookie dough onto the prepared tray.
Remove the frangipane from the refrigerator and divide it evenly into tablespoon-sized portions (one for each dough ball). If at any point the frangipane becomes too sticky to handle, place it in the fridge or freezer to chill.
Assemble. When ready to assemble, take a ball of cookie dough and flatten it between your hands. Place a sphere of filling in the center, then fold the edges of the dough up and over the almond filling, pinching to seal. Gently roll the dough between your hands until smooth.
Roll the top of each cookie into the sliced almonds, pressing gently so they stick. Repeat with the remaining balls of cookie dough.
Place the shaped cookies on the prepared baking sheet, cover with plastic wrap, and chill for at least 2 hours (ideally overnight). Alternatively, freeze for 1 hour.
Bake. When ready to bake, preheat oven to 350°F and line a large baking sheet with parchment paper. Remove the dough from the fridge and arrange onto the pan at least 2'' apart.
Bake the cookies for 14-16 minutes, until just golden at the edges. Remove the tray from the oven and let cool for 5 minutes, then transfer the cookies to a wire rack. Repeat with the remaining dough.
Once cooled, dust the cookies with powdered sugar and serve.