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1
Preheat oven to 400 degrees F (200 degrees C). Grease and flour the bottom of a 15x20-inch rimmed baking sheet or jelly roll pan, or line it with parchment paper.
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2
Sift white sugar and flour together in a bowl.
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3
Combine hot water, creamy peanut butter, and 1/2 cup butter in a saucepan; bring to a boil, stirring frequently. Remove from heat.
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4
Blend yogurt, eggs, and baking soda together in a bowl. Pour peanut butter mixture into egg mixture in a steady stream, stirring constantly. Mix flour mixture into peanut butter mixture until batter is combined. Spread batter into prepared baking sheet.
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5
Bake in preheated oven until the center of the cake springs back when touched lightly with a fingertip, about 20 minutes. Cool on wire rack.
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6
Combine chunky peanut butter, 1/2 cup butter, and 6 tablespoons milk in a small saucepan; bring to a boil, stirring constantly. Reduce heat to low; stir in confectioners' sugar and maple syrup until sugar dissolves and frosting is smooth. Pour warm frosting over warm cake. Sprinkle walnuts, pecans, and almonds over the top; cool completely.
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7
Stir cream cheese, 1/2 cup confectioners' sugar, and 1 tablespoon milk together in a bowl until smooth; add almond extract. Fold whipped topping into cream cheese mixture until frosting is creamy and runny. Drizzle cream cheese frosting over the top of cooled cake.
