Preheat the oven to 350 degrees F. Spray a 17x12 or 18x13 inch sheet pan with non-stick cooking spray and set aside.
Combine the dry ingredients: In a large bowl sift together 2 cups all-purpose flour, 2 cups granulated sugar, 1 teaspoon baking soda, and ½ teaspoon salt. Set aside.
Make the cocoa mixture: In a large saucepan, melt 1 cup (2 sticks) unsalted butter over medium heat. Once melted, whisk in ⅓ cup cocoa powder until smooth. Carefully pour in 1 cup boiling water. Stir and bring the mixture to a boil. Let it bubble for about 1 minute, then remove from the heat.
Combine the wet and dry ingredients: pour the cocoa mixture into the bowl with the dry ingredients. Stir until everything is well combined.
Mix the milk and eggs: in a separate bowl or large measuring cup, stir together ½ cup milk and 1 tablespoon vinegar. Let it sit for about 3 minutes then whisk in 2 large eggs, lightly beaten, and 2 teaspoons vanilla extract. Pour this mixture into the cake batter and stir until smooth and fully combined.
Bake the cake: pour the batter into the prepared sheet pan. Bake for about 20 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool completely before frosting.