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Preheat oven to 350°F with racks in upper and lower thirds. Butter sheet pans, then line bottoms with parchment paper and butter parchment. Dust with flour, knocking out excess.
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Break up almond paste with your fingers into a food processor. Pulse until coarsely ground, then add 1/4 cup sugar, 1/4 cup flour, and 1/4 tsp salt and process until very finely ground.
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Transfer mixture to a large bowl and whisk in yolks, milk, and extracts.
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Beat egg whites with a pinch of salt in a bowl with an electric mixer at medium speed until they hold soft peaks. With mixer at low speed, add remaining 1/2 cup sugar in a slow stream. Beat at medium-high speed until whites hold stiff, glossy peaks. Fold one third of whites into batter to lighten, then fold in remaining whites gently but thoroughly. Fold in remaining 3/4 cup flour.
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Divide batter between pans, spreading evenly, and rap pans against counter a couple of times to release any air bubbles. Bake cakes, switching position halfway through, until pale golden and springy to the touch, 16 to 18 minutes.
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Cool in pans until warm. Invert onto racks lined with parchment. Carefully peel off parchment from tops and cool completely.
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While cake layers cool, pulse preserves in cleaned food processor until smooth.
