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Preheat the oven to 350°F. Lightly grease two 8" or 9" round pans. For extra protection against sticking, dust the pans with flour or line the bottoms with parchment and grease the parchment. Note: Make sure your 8" pans are at least 2" deep; if they're not, use 9" round pans or another of the pan options listed in "tips," below.
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Using a stand mixer set on low speed, mix all the dry ingredients until thoroughly combined. Add the soft butter and mix until evenly crumbly, like fine, damp sand.
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Beat in the egg whites one at a time then the whole eggs, beating for about 30 seconds and scraping down the sides and bottom of the bowl after each addition. This process helps build the cake’s structure.
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In a small bowl or measuring cup, whisk the milk with the vanilla and almond extracts. Add this milk mixture, one-third at a time, to the batter. Beat for 30 seconds and scrape down the sides of the bowl after each addition. The batter may look a little curdled; that’s OK.
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After you’ve scraped the bowl one final time, beat for an additional 30 seconds.
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Pour the batter into the prepared pans. Bake for 30 to 35 minutes, until set and starting to pull away from the edges of the pans. A toothpick or paring knife inserted into the center of a cake will come out with a few moist crumbs sticking to it when it’s done.
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Remove the cakes from the oven and cool for 15 minutes in the pans. Transfer the cakes to a rack to cool completely before frosting and serving.
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Storage instructions: Store leftover cake at room temperature, well-wrapped, for up to three days; in the refrigerator, covered, for up to a week, or in the freezer, well wrapped, for up to a month.