Preheat your oven to 350°F. Lightly spray a 9x12 baking pan with cooking spray or grease it with butter. Set it aside.
In a large bowl, blend together the yellow cake mix, 3 large eggs, 1/3 cup vegetable oil, 1/2 cup peach nectar (and the drop of food coloring if using) until well combined. It should be smooth with no dry streaks — about 30 seconds with a whisk. Don't overmix.
Gently fold the chopped peaches into the batter with a spatula. Overmixing at this stage can break up the peaches and make the cake dense. Just a few folds until they're evenly distributed.
Pour the batter into the prepared pan and spread it evenly. Bake for 28 minutes, or until done — test with a toothpick inserted in the center; it should come out without wet batter clinging to it, but a few moist crumbs are fine. The sides will just start to pull away from the pan. Let the cake cool in the pan on a wire rack for exactly 5 minutes while you make the frosting.
While the cake bakes, combine 1/2 cup unsalted butter (cut in pieces), 1/2 cup heavy cream, and 1 cup packed brown sugar in a medium saucepan. Bring to a boil over medium heat, stirring constantly. Once it reaches a full rolling boil — large bubbles that don't stop when you stir — let it boil for a full minute. Remove from heat and add 1 teaspoon vanilla extract and the sifted 2 1/2 cups confectioner's sugar. Whisk vigorously until the frosting is smooth and all lumps are gone. If it's too thick or lumpy, put it back on low heat for a few seconds and whisk again — but don't let it boil.
Working quickly, pour the frosting over the warm cake (the 5-minute rest is perfect). Tilt the pan gently to spread it evenly if needed — but try to get it right on the first pour, because the frosting sets fast and you won't be able to spread it without cracking the surface.
Let the frosting set at room temperature until firm, about 30 minutes. If you're in a hurry, pop the pan in the refrigerator for 15 minutes. Once set, slice with a sharp knife — the top will crackle perfectly.