Preheat the oven to 350°F. Butter the sides of the cake pan and line the bottom with parchment paper.
Put the almonds, granulated sugar, Fleur de Sel, Pure Almond Extract and Pure Vanilla Extract in the food processor and process until the nuts are finely pulverized. Add the butter and pulse until blended. Add the eggs and process until thoroughly blended. Add the flour and baking powder and pulse just until incorporated, scraping the bowl once with a spatula.
Scrape the batter into the prepared pan and spread it evenly. Bake for 35 to 40 minutes, until the cake is golden brown on top and a toothpick inserted in the center comes out clean. Cool completely in the pan on a rack.
To unmold, slide a butter knife or offset spatula around the sides of the cake to release it. Cover the cake with a serving platter and invert. Remove the pan, peel off the parchment liner, and turn the cake right side up. Wrapped airtight, the cake keeps well at room temperature for several days, or in the freezer for up to 3 months; bring to room temperature before serving.
Dust the cake lightly with powdered sugar before serving.