Cream together the butter (1/2 lb.) and sugar (1.5 cups) until fluffy with an electric mixer on high speed for about 1 minute.
Add the egg and mix on high speed for about another minute.
Add the almond extract and vanilla extract (1 teaspoon each) and mix until combined.
Add the flour (2 cups) and mix until combined. The dough will be thick and sticky. Use a spatula to scrape down the sides of the bowl to place all the dough in the center of the bowl. Use a butter knife to cut down the center of the dough, to divide into two equal portions.
Mix together the 2 tablespoons water and the egg yolk with a fork until smooth. Set aside.
Place the 2 dough portions in 2 ungreased 8-inch cake pans. Press down with your hands, or using an offset spatula, to flatten and smooth out the dough as best you can, filling the bottom of the cake pan all the way to the edges.
Brush the tops of each cake with the egg yolk mixture. I recommend brushing each of them 2-3 times, allowing the egg to be absorbed into the top layer while you alternate back and forth, using all or almost all of the yolk mixture.
Sprinkle the top of each cake with the sliced almonds (1/4 cup for each cake). Press the almonds down gently, so they are in a single layer and are adhered to the top of the cake. It's OK, and actually a good thing, if the egg yolk mixture gets on top of the almonds.
Bake at 350 degrees F for 30-40 minutes, or until deeply golden on the edges and slightly golden all across the top.
Cool in pan for at least 45 minutes. Remove and cut each into 12-16, depending on how big you want them. Store in an airtight container at room temperature for 4-5 days, or in the fridge for 7-10 days.
If using unsalted butter, I recommend adding 1/4 teaspoon of kosher salt to the batter when you add the sugar.
If you don't have 8-inch cake pans, 9-inch can be used. The cakes will come out thinner and may crumble more easily but are still delicious! Bake for 25-35 minutes, as they may need less time.
For a nut-free version, omit the almonds on top. Use the tines of a fork to carve lines on top of the cake before brushing the egg wash mixture on top, then bake as directed. Nielsen-Massey Pure Almond Extract is allergen-free, so those with nut allergies are still able to use it.
Freezer directions: Freeze the cake whole, wrapped tightly in plastic wrap, nestled into the cake pan, then thaw at room temperature for 12-24 hours. Alternatively, you can flash freeze the sliced cake- place the slices on a baking sheet and freeze for 20 minutes, then place the slices into an airtight container or plastic bag and store in the freezer. Lasts for 3 months in the freezer.