Preheat the oven to 350 degrees F. Grease a 13 by 17-inch sheet pan and line the bottom and sides with parchment or waxed paper.
Sift together the 3 cups of sugar, the flour, cocoa, baking powder, baking soda, and salt. Transfer to a mixer fitted with a whisk attachment (or use a hand mixer) and blend briefly.
Whisk together the eggs, milk, oil, and vanilla extract in a medium bowl. Add to the dry ingredients and mix at low speed for 5 minutes. Gradually add the hot water, mixing at low speed just until combined. The batter will be quite thin.
Pour the batter into the pan. Bake until a tester inserted in the center of the cake comes out clean (a few crumbs are okay) and the center feels firm to the touch, 25 to 30 minutes. Let cool in the pan. Chill, covered, until ready to cut the cake.
With the heart cutter, cut out hearts and place them on a sheet pan.
To make the marshmallows: Combine the 1/4 cup water, the corn syrup, and the sugar in a saucepan fitted with a candy thermometer. Bring to a boil and boil to "soft-ball" stage, or about 235 degrees F.
Meanwhile, whip the egg whites until soft peaks form.
Sprinkle the gelatin over the 2 tablespoons water and let dissolve. When the syrup reaches 235 degrees F, remove it from the heat, add the gelatin, and mix.
Pour the syrup into the whipped egg whites. Add the vanilla and add a few drops of red food coloring to turn it pink and continue whipping until stiff.
With a large plain tip in a pastry bag, pipe marshmallow on half the cake hearts to cover the surface entirely. Top with remaining cake hearts to form sandwiches. On top of the cakes, pipe 2 teardrops in a V meeting at the bottom to form a heart. Sprinkle the marshmallow lightly with red sugar.