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Preheat oven to 350 F.
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Line an 8x8 (or 9x9) baking pan with aluminum foil (or you may butter and flour it).
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In processor, add half of cooled, toasted whole almonds and grind until fine crumbs (still a little coarse and dry to the touch. Do not overgrind or they will turn into a paste!)
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Transfer ground almonds to a mixing bowl.
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Grind remaining almonds and add them to the bowl.
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Add flour, baking powder, and salt to ground almonds. Mix until evenly distributed.
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In a stand mixer, or in a large bowl with an electric mixer, beat eggs at high speed until foamy, about 15 seconds, adding sugar a little at a time.
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Throughout the whole mixing process, scrape down the sides of the bowl as needed to incorporate all ingredients.
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Continue beating until mixture is thick, pale, and just starts to form a ribbon when the beater is lifted out (7-8 minutes in a stand mixer, 10-14 minutes with a handheld).
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Add melted butter in a slow stream, beating constantly.
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Add milk and almond extract and beat until just combined.
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Reduce speed to low, then add flour mixture, mixing until just combined.
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Spread batter into prepared baking pan, and smooth out top with scraper.
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Sprinkle on sliced almonds over surface of cake.
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Bake cake about 35-40 minutes, or until top is golden brown, and a toothpick inserted into the center of the cake comes out clean.
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Cool cake for 10 minutes, then (if using tinfoil), once not hot to the touch, lift cake by tinfoil and set on rack to cool about another 20 minutes and then invert cake onto rack. If not using tinfoil, Let cake cool for 30 minutes in pan on rack before removing. When removing, run a knife along the edges to loosen the cake and invert onto rack.
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Turn cake right-side up and continue to cool completely, about another 30 minutes.