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Preheat the oven to 350°F. Grease and flour (or line with parchment paper) three 9" cake pans.
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To make the cake: In a large bowl, stir together the flour, sugar, cocoa, salt and baking soda.
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In a separate bowl, beat together the vanilla extract, almond extract, vinegar, vegetable oil, and water.
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Add the liquid ingredients to the dry ingredients, beating until well combined.
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Divide the batter among the pans.
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Bake the cakes for 35 to 40 minutes, or until a toothpick inserted into the center of one comes out clean.
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Remove the cakes from the oven, and cool completely before frosting. If desired, the unfrosted cake layers can be tightly wrapped and frozen for up to 3 months, then thawed and decorated.
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To make the frosting: Put the peanut butter and vanilla into a large mixing bowl and mix at low speed. With the mixer running Add 1 cup of confectioners' sugar followed by 2 tablespoons of almond milk, stopping to scrape the bowl from time to time. Continue adding and alternating 1 cup of confectioners' sugar with 2 tablespoons of almond milk until you have used up all of both ingredients. The frosting's consistency should be on the stiff side, a little stiffer than the peanut butter by itself.
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To assemble the cake: Trim off any domes on the layers. Place one layer on a serving plate trimmed side down. Peel off the parchment, and spread with 1 cup of the frosting, spreading to the edge but not covering the sides. Repeat with the remaining two layers.
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Store cake at room temperature, covered, for several days.