1. Preheat the oven to 325ºF (160ºC). Grease a 9- or 10-inch (23-25 cm) cake or spring form pan with butter, dust it with flour and tap out any excess. Line the bottom of the pan with a round of parchment paper. (See Note, below.)
2. In the bowl of a food processor, grind the sugar, almond paste, and 1/4 cup (35g) of flour until the almond paste is finely ground and the mixture resembles sand.
3. In a small bowl, whisk together the remaining 3/4 cup (105g) of flour, baking powder, and salt.
4. Once the almond paste is completely broken up, add the cubes of butter and the vanilla and almond extracts, then process until the batter is very smooth and fluffy.
5. Add the eggs one at a time, processing a bit before the next addition. (You may wish to open the machine and scrape the sides down to make sure the eggs are getting fully incorporated.) After you add all the eggs, the mixture may look curdled. Don’t worry; it’ll come back together after the next step.
6. Add half the flour mixture and pulse the machine a few times, then add the rest, pulsing the machine until the dry ingredients are just incorporated, but do not overmix. (You can also transfer the batter to a bowl and mix the dry ingredients in, which ensures the dry ingredients get incorporated evenly and you don’t overbeat it.)
7. Scrape the batter into the prepared cake pan and bake the cake for 45-60 minutes, or until the top is deep brown and feels set when you press in the center.
8. Remove the cake from the oven and run a sharp or serrated knife around the perimeter, loosing the cake from the sides of the pan. Let the cake cool completely in the pan.
Once cool, tap the cake out of the pan, remove the parchment paper, and set on a cake plate until ready to serve. (Tip: Warm the bottom of the cake pan directly on the stovetop for just a few seconds, which will help the cake release.)