Press half of the cookie dough in your baking tin. This layer will be very thin. Spread all of the frangipane into an even layer on top of the cookie dough.
Grab pieces of the remaining cookie dough and flatten them into discs in the palm of your hands. They should be around 1/4 inch (6mm) thick. Arrange the dough on top of the frangipane. Crumble any remaining cookie dough in the gaps. If desired, gently smooth the surface of the cookie dough. Sprinkle the almonds on top.
Bake the cookie bars for 30-35 minutes (less time for gooeier bars, more time for crunchier bars). The cookie bars are ready when the surface is slightly golden brown and the edges look set. If you insert a toothpick in the center, it should come out mostly clean with a few moist crumbs (but no wet batter). The bars may puff up in the oven, but will settle when they cool.
Allow the cookie bars to cool in the tin on a wire rack for at least 1 hour. Then use the parchment paper to lift the bars out of the pan and let them cool on the wire rack. When the slab is completely cool, cut it into squares with a serrated knife.
Store leftover cookie bars in an air-tight container at room temperature for up to 5 days, in the fridge for up to 10 days or in the freezer for up to 1 month.