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1
Dissolve espresso powder in a bowl with 2 tablespoons hot water.
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2
Preheat oven to 350 degrees F (175 degrees C). Grease two 8-inch cake pans.
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3
Beat white sugar, 1/2 cup butter, and brown sugar together in a bowl using an electric mixer until light and fluffy, about 3 minutes. Add eggs 1 at a time, blending well after each. Reduce mixer speed to low. Beginning and ending with flour, alternate adding flour and buttermilk in 5 rounds. Blend 2 teaspoons dissolved espresso into the batter.
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4
Dissolve baking soda in the vinegar in a bowl; add to the batter. Mix until incorporated. Divide the batter equally between the prepared pans.
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5
Bake in the preheated oven until golden brown, 32 to 35 minutes. Cool in the pans on a wire rack for at least 20 minutes before removing from pans and cooling completely, about 40 minutes more.
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6
Place 1 1/2 plus 2 tablespoons butter in the bowl of an stand mixer with a whisk attachment. Whip on medium-high speed until smooth. Add confectioners' sugar and mix on medium-low until combined. Add salt, whipping on medium-high until smooth. Mix in heavy cream and vanilla extract on low until incorporated. Whip on high until frosting is light and fluffy, scraping down the bowl as needed.
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7
Divide frosting into 5 equal portions. Leave 2/5 (2 portions) plain. Add remaining 2 teaspoons espresso mixture to another 2/5 (2 portions); stir until well blended. Add 2 tablespoons of caramel topping to the remaining 1/5 (1 portion); stir until well blended.
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8
Level both cakes and place 1 on a platter. Spread 3 tablespoons of the remaining caramel sauce over it and top with a layer of espresso frosting. Place other cake on top. Spread a thin layer of vanilla frosting on the cake to seal in any crumbs; chill for 30 minutes.
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9
Frost cake again with a thin layer of espresso frosting. Pipe vanilla frosting around the top edge. Fill the center with caramel frosting. Drizzle generously with the remaining caramel sauce.
