For the Cake,

Preheat oven to 325°F (170°C). Spray an 8-inch square baking pan with baking spray with flour. Cut a sheet of parchment paper into at least a 16¼x8-inch rectangle. Fold in half widthwise. From center fold, fold over a 2-inch section. Place parchment in prepared pan with 2-inch section standing up in center to form a divider.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter and granulated sugar at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in vanilla extract.

In a medium bowl, whisk together flours, baking powder, and salt. With mixer on low speed, gradually add flour mixture to butter mixture alternately with ¼ cup (60 grams) cream, beginning and ending with flour mixture, beating just until combined after each addition. Transfer half of batter (about 2 cups or 472 grams) to another medium bowl; fold in 2 tablespoons (30 grams) cream just until combined.

In a small bowl, whisk together cocoa, red food coloring, and remaining 2 tablespoons (30 grams) cream until smooth. Fold cocoa mixture into remaining batter until combined. With the plain batter, add mint or peppermint extract and green food coloring and fold to combine. Spoon each batter into one side of prepared pan. Using a small offset spatula, smooth flat; run tip of spatula through each batter. Tap pan on a kitchen towel-lined counter to help release air bubbles.

Bake until a wooden pick inserted in center of each cake comes out clean, 40 to 50 minutes. Let cool in pan for 10 minutes. Remove from pan, and let cool completely on a wire rack. Using a serrated knife, trim each cake into 2 approximately 7½x1½x1½-inch rectangles. Continue to slice each rectangle into another 4 even long pieces, approximately 71/2 x 1/3×1/3 rectangles.

In another small bowl, whisk jam until smooth.

Lightly dust a work surface with confectioners’ sugar. On sugar-dusted surface, roll Vanilla Marzipan into a 13½x9½-inch rectangle (about ⅛ inch thick). (You can turn the marzipan over before building the cake if you do not want any confectioners’ sugar to be on the outside of the cake.) Spread jam on one side of one piece of mint cake, and place, jam side down, on marzipan; spread jam on remaining sides of mint cake piece. Spread jam on one side of one piece of red velvet cake, and place, jam side down, next to vanilla cake piece on marzipan. Continue this step until 4 pieces of cake are at the base. Spread jam on exposed sides of cake pieces. Repeat the next layer the same way but alternating colors against the previous layer. Continue until there are 4 layers of cake. Spread jam on all exposed sides of cake piece. Gently press all cake pieces together.

Trim marzipan flush with ends of cake. Carefully wrap marzipan around cake, gently pressing to smooth out air pockets and seal. Trim off any excess marzipan if there is any overlap. Place, seam side down, on a serving platter, and refrigerate for at least 30 minutes. Before serving, score marzipan in a checkerboard pattern, and trim each end. Place the nonpareils at the cross section of each checkerboard pattern for additional decoration if desired.

For the Marzipan,

In the work bowl of a food processor, place confectioners’ sugar, flour, and salt; pulse until combined. Add egg white and vanilla, and process until mixture holds together and has the consistency of softened butter.

Lightly dust work surface with confectioners’ sugar. Turn out marzipan, and knead until smooth and no longer sticky, dusting with confectioners’ sugar as needed. Shape into a rectangle, and wrap tightly in plastic wrap. Refrigerate for at least 1 hour before using.