Preheat oven to 350°F (180°C). Butter a 17¼x12½-inch rimmed baking sheet. Line bottom of pan with parchment paper, and dust sides with cocoa, tapping out excess.

In a very large bowl, sift together flour, cocoa, baking soda, espresso powder, baking powder, and salt. Whisk until well combined.

In a large bowl, whisk together sugar, yogurt, oil, cream, eggs, egg yolks, vanilla bean paste, and peppermint extract. Gradually add sugar mixture to flour mixture, whisking just until combined and stopping to scrape sides of bowl. Gradually pour in hot coffee, whisking until combined and stopping to scrape sides of bowl. Spread batter into prepared pan. Tap pan on a kitchen towel-lined counter a few times to settle batter and release any air bubbles.

Bake until a wooden pick inserted in center comes out clean, 16 to 22 minutes. Using a small offset spatula, loosen edges of warm cake. Let cool completely in pan. Freeze in pan for 30 minutes. (See Note.)

Using a small offset spatula, gently loosen edges of frozen cake. Place a piece of parchment paper on top of cake; invert cake onto a very large cutting board or an upside-down baking sheet, and discard original parchment. Using a serrated knife, trim cake into a 16x11-inch rectangle. Cut cake in half crosswise to create 2 (11x8-inch) rectangles, cutting through parchment underneath.

Using parchment to help support, gently turn 1 rectangle onto a serving plate; discard parchment. Dollop 2¼ cups (458 grams) Mint Chip Buttercream onto bottom half of cake; spread into an even layer using the back of a spoon or a small offset spatula.

Using parchment to help support, gently turn remaining cake half onto buttercream layer, being sure to line up edges of cake; discard parchment. Dollop and spread remaining Mint Chip Buttercream on top of cake, swirling and swooping with back of a spoon as desired. Garnish with chocolate, if desired.