Preheat your oven to 350°F (175°C). Grease a 13x18-inch baking sheet with butter or nonstick cooking spray and line the bottom with parchment paper.
In a large mixing bowl or the bowl of a stand mixer, combine 2 cups all-purpose flour, 2 cups granulated sugar, 1/3 cup cornstarch, 1/3 cup unsweetened cocoa powder, 2 teaspoons baking soda, 1 teaspoon baking powder, and 1 teaspoon salt. Mix on low speed until well incorporated.
Add 2 large eggs, 1 cup buttermilk, 3/4 cup warm water, 1/3 cup vegetable oil, 3/4 teaspoon vanilla extract, 3/4 teaspoon distilled white vinegar, and 1 1/2 tablespoons red food coloring. Beat on medium speed for about 2 minutes, or until the batter is smooth.
Pour the batter into the prepared baking sheet and spread it evenly.
Bake for 30 to 35 minutes, or until a toothpick inserted in the center comes out clean. Allow the cake to cool completely in the pan before frosting.
Frosting
To make the frosting, beat the 8 ounces cream cheese (softened) and 1/2 cup salted butter (softened) in a large bowl with a hand mixer or stand mixer until light and fluffy, about 2-3 minutes. Add the 1/2 teaspoon vanilla extract and mix until combined. Gradually beat in the powdered sugar, 1 cup at a time, until the frosting is smooth. Add milk as needed to acheive a spreadable consistency.
Spread the frosting evenly over the cooled cake. Slice and serve.
Notes
For a brighter red color, reduce the cocoa powder to 1/4 cup.