Special equipment: a quarter sheet pan (13 by 9 inches); a 2- or 3-inch heart cookie cutter
For the cake: Place a rack in the lower third of the oven and preheat to 325 degrees F. Butter and flour a 9-by-4 1/2-inch loaf pan and a quarter sheet pan (13 by 9 inches).
Sift the flour and salt into a medium bowl; set aside. Whisk the whole eggs, yolks, milk and vanilla together in a medium bowl; set aside. Beat the butter in a stand mixer fitted with the paddle attachment at medium speed until smooth, about 1 minute. Gradually add the granulated sugar 1/4 cup at a time until well combined. Turn the machine off and scrape down the paddle and sides of the bowl with a rubber spatula. Continue to beat the butter mixture on medium speed until light and fluffy, about 4 minutes.
Turn the machine off and scrape the sides of the bowl again. Turn the mixer to its lowest setting and gradually add in the flour mixture 1/4 cup at a time until just combined. Slowly add the egg mixture. Remove the bowl from the mixer, scrape any batter off the paddle and make sure the batter is well combined. (Take care not to overmix.)
Divide the batter in half. Fold the red food coloring into one half and the green into the other half with a rubber spatula until no streaks remain.
Pour the red batter into the prepared quarter sheet pan and bake until set, but slightly under-baked, about 18 minutes.
Turn the cake out onto a parchment-lined surface. Let cool slightly, then cut 12 hearts out of the sheet cake with a 2- or 3-inch heart cookie cutter.
Pour enough green batter into the prepared loaf pan to just cover the bottom. Nestle the hearts point-end down in a row down the center of the batter, so that they snugly fit the length of the pan. Spoon the remaining batter on top and smooth the top with a rubber spatula. Bake until a toothpick inserted into the center comes out clean and the top springs back when lightly pressed, 50 minutes to 1 hour.
For the glaze: Meanwhile, whisk together the confectioners' sugar, milk and vanilla in a medium bowl to make a thick but pourable glaze.
Cool the cake in the pan on a rack set into a rimmed baking sheet, 10 to 15 minutes. Invert the cake onto a plate. Re-invert the cake and set it right-side up on the rack. Pour the glaze over the cake while still warm, allowing excess glaze to drip into the pan below. Allow the cake to cool completely. Slice into the cake to reveal the heart inside.
The cake will keep wrapped in plastic wrap at room temperature for 4 to 5 days, and freezes well for up to 1 month.
Combine the beet juice, beet powder and cocoa powder in a small bowl and whisk until smooth. Combine the matcha powder with 3 tablespoons water in another small bowl and whisk until smooth. Use the beet coloring in place of red food coloring and the matcha coloring in place of green coloring in the Hidden Heart Cake.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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