Special equipment: a 18-by-13 rimmed sheet pan, a large cake board or cutting board, 2-inch round cutter, pastry bag and pastry brush
For the cake: Preheat the oven to 350 degrees F. Coat a 18-by-13 rimmed sheet pan with cooking spray, then line with parchment and spray the parchment.
Combine the cake mix and pudding mix in a stand mixer fitted with the paddle attachment and mix on low speed to blend. With the speed still on low and add the egg whites, 3/4 cup water and vegetable oil and mix until combined. Raise the speed to medium and mix until increased in volume, lighter in color and smooth, about 5 minutes.
Pour the batter into the prepared baking sheet; smooth into an even layer using an offset spatula.
Bake until golden on top and the edges pull away from the pan, about 15 minutes. Transfer to a rack and let cool completely on the baking sheet, then refrigerate until firm, about 15 minutes.
For the Swiss buttercream: Meanwhile, bring a few inches of water to a boil in a saucepan that can hold a heatproof stand mixer bowl above the water without the bottom of the bowl touching.
Add the sugar, lemon juice, salt and egg whites to the mixing bowl, and whisk together by hand. Set the bowl above the boiling water and whisk until the mixture is warm to the touch and the sugar completely dissolves. Transfer to the stand mixer fitted with the whisk attachment and beat at medium-high speed until cool and the whites hold stiff peaks, 10 to 15 minutes.
Toss in a couple of chunks of butter at a time, making sure the pieces are incorporated before adding more. After all the butter is added, continue whisking on medium-high speed. The mixture will deflate and appear curdled. Continue whisking until the buttercream comes back together to form a smooth and spreadable consistency. Slowly drizzle in the vanilla while beating until smooth and light. (If the frosting is very soft or begins to break, refrigerate until set but still spreadable and then beat until light before using.)
Transfer half of the buttercream to a large microwave-safe bowl. Stir in drops of yellow, orange and ivory food coloring with a rubber spatula to tint the color of "yellow cheese." Transfer a quarter of the remaining buttercream to a second microwave-safe bowl. Stir in drops of red and ivory food coloring for the "tomato sauce." Add the remaining buttercream to a third bowl and tint ivory for the crumb coat (the first layer of frosting on the cake), "filling" and "crust".
To assemble the cake: Lightly coat the cake with cooking spray, then cover with parchment and invert onto a cutting board.
Cut cake into triangles: With the cake oriented vertically (one of the short sides nearest you) run a sharp paring knife from one of the corners nearest you to the center of the far short edge of the cake. Do the same from the other near corner to divide the cake into one large triangle and two smaller adjoining triangles.
With a large offset spatula, carefully lift the large triangle onto a cake board. Coat the top and sides with a thin layer of ivory buttercream. Flip the two smaller triangles, side-by-side with the cut-sides facing out, onto the larger triangle to form a second cake layer.
Using a serrated knife, trim 1 1/2-inches from the short side (the "crust" end) of the cake, angling the knife to reproduce the curve of a pizza pan. Gather up the cake scraps and squeeze them into a dough. Roll the dough into a rough 1-inch log and press it into crust end of the cake to form the raised lip of the pizza crust.
Using an offset spatula, spread a thin crumb coat layer of ivory buttercream all over the cake. Chill until firm, about 20 minutes.
Generously frost the sides and crust with more ivory buttercream. Pipe a small mound of buttercream onto the crust to look like a dough bubble. Refrigerate until firm, about 10 minutes.
Dilute 2 drops ivory food coloring with the alcohol spirits. Dip a pastry brush in the mixture and using a light hand, brush the crust and sides of the cake light brown.
Microwave the red buttercream in 15 second intervals, stirring in between, until slightly melted. Transfer to a pastry bag without a tip and pipe an irregular "sauce" along the base of the crust and slightly up the lip.
Set aside a quarter of the yellow buttercream. Microwave the remaining in 15 second inncrements, stirring in between, until melted. Whisk the reserved yellow buttercream back in until blended. Transfer to a pastry bag without a tip and pipe a thick, wavy layer of "cheese" onto the top of the pizza slice, overlapping the tomato sauce in spots. Pipe cheese over the edges of the slice to look like drips of melted cheese.
Spread the fruit rollups flat on a cutting board and stamp out "pepperoni" circles using a 2-inch round cutter sprayed with cooking spray. Top the pizza with as much pepperoni as you like.
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