Preheat oven to 300 degrees. Line a 17-by-12-inch rimmed baking sheet with a nonstick baking mat and set aside.
In the bowl of an electric mixer fitted with the whisk attachment, whisk together eggs and sugar until pale and thick (the whisk should hold a ribbon-like train on the surface when raised). Add mayonnaise and vanilla paste and whisk until fully incorporated.
In a medium bowl, whisk together flour, baking soda, baking powder, and salt. Transfer flour mixture to a fine-mesh sieve and sift ingredients into a medium bowl. With the mixer on low, add flour mixture to egg mixture in three additions, alternating with 1 1/2 cups plus 1 tablespoon water, mixing well after each addition.
Transfer batter to prepared baking sheet. Bake until a cake tester inserted into the center comes out clean, 20 to 25 minutes. Let cool in baking sheet on a wire rack. Using a 3 1/2-inch heart-shaped cutter, cut out 12 hearts. Using a 1-inch heart-shaped cutter, cut out the center of each of the larger hearts, taking care not to cut all the way through; discard centers. Transfer each cake to a plate.
Fill the center sections of each heart with 1 tablespoon passion-caramel filling and top each with 1 tablespoon marshmallow filling. Fill a pastry bag fitted with a 3/4-inch round tip (Wilton No. 809) with chocolate icing; pipe icing over filling.
Place fondant on a nonstick baking mat; press your thumb into the center of the fondant to make a well. Add 5 drops of food coloring in the well and knead fondant until color is well blended. Working with about 6 tablespoons fondant at a time, roll out into a 14-inch circle about 1/8-inch-thick. Cut out a 13-by-13-by-13-inch triangle from the circle.
Drape fondant triangle over one of the heart-shaped cakes with the 4-inch side draped over the widest part of the heart. Using your fingers, press fondant to adhere; trim edges. Repeat process with remaining fondant and cakes.
Gather scraps of fondant and place on a nonstick baking mat; press your thumb into the center of the fondant to make a well. Add 5 drops of food coloring in the well and knead until color is well blended. Roll out fondant 1/8-inch thick; using a 1/2-inch heart-shaped cutter, cut out 12 hearts. Place a heart on each cake and tie a brown ribbon around the bottom edge of each cake, if desired. Serve immediately.
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