• Preheat the oven to 350°F. Brush two 8-inch baking pans with unsalted butter and dust them with gluten-free all-purpose flour. Place a circle of parchment paper at the bottom of each pan and set aside.
• Whisk together the gluten-free all-purpose flour, dark cocoa powder, baking soda, baking powder, and salt in a medium bowl. Set aside.
• Mix the milk, white vinegar, peppermint extract, and vanilla extract in a measuring cup. Set aside.
• Place the granulated sugar and butter in a mixing bowl. Using a stand mixer with the paddle attachment or a hand mixer, beat on high speed until light and fluffy, about 2 minutes. Turn off the mixer and scrape down the sides of the bowl. Add the eggs one at a time, scraping down the bowl after each addition.
• Add one-third of the dry ingredients to the mixing bowl and mix on low speed just until combined. Turn off the mixer and scrape down the sides of the bowl. Add half of the milk mixture and mix on low speed just until combined. Turn off the mixer and scrape down the sides of the bowl. Add another one-third of the dry ingredients and mix until combined. Turn off the mixer and scrape down the sides of the bowl. Add the remaining milk mixture and mix on low speed just until combined. Turn off the mixer and scrape down the sides of the bowl. Finish by adding the remaining dry ingredients and mix until just combined.
• Using a spatula, fold in the melted chocolate. Divide the batter evenly between the two cake pans. Let rest for 10 minutes. Place the pans in the oven and bake for 35–40 minutes, or until the cake bounces back when gently pressed in the center or a toothpick inserted in the center comes out clean.
• Remove from the oven and place on a cooling rack for 10–15 minutes. Turn the cakes out onto the cooling rack and let cool completely.

Peppermint Cream Cheese Frosting

• Place the cream cheese in a large mixing bowl. If using a stand mixer, use the whisk attachment. Beat on medium speed until the cream cheese is smooth and beginning to become fluffy. Add the butter and mix until well combined.
• Add the powdered sugar, peppermint extract, and salt to the bowl. Mix on low speed until the sugar is incorporated. Turn off the mixer and scrape down the sides of the bowl. Turn the mixer to high speed and whip until light and fluffy. Turn off the mixer, scrape down the bowl again, then whisk on high speed for 1–2 minutes until the mixture is smooth and well incorporated.

Suggested Cake Decoration

• Place about half of the frosting in a medium bowl. Whisk in ½ teaspoon of red food coloring or 4–5 drops of red gel food coloring until you reach the desired shade of red.
• To ice the cake, place the red frosting in a piping bag or large zip-top bag. Place the white frosting in another piping bag or large zip-top bag. Cut the end of each bag (or corner of the zip-top bags) to create a ½-inch opening.
• To frost the cake, cut each cake in half crosswise to create four layers. Place the bottom layer on a cake stand or plate, and set it on a turntable if available. Starting with the white frosting, pipe a circle around the outer edge of the bottom layer. Next to the white frosting circle, pipe a circle of red frosting. Continue alternating white and red frosting circles until the entire layer is covered. Repeat with the remaining three layers, then place the final cake layer on top.
• Chill the cake until the center frosting layers are firm, about 15 minutes. Frost the outside of the cake with white frosting to create a crumb coat, then repeat the frosting layers until no cake is visible. Refrigerate the cake between frosting layers for about 15 minutes each time.
• Pipe small dots of red frosting onto the outside of the cake and gently spread to create a tie-dye effect. Sprinkle crushed candy canes around the top edge and the base of the cake. Refrigerate until ready to serve.