Preheat the 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, stir together 2 cups all-purpose flour, 2 cups granulated sugar, 1/2 cup unsweetened cocoa powder, 2 teaspoons baking soda, 1 teaspoon baking powder, and 1 teaspoon salt. Mix until well combined.
Add 2 large eggs, 1 cup buttermilk, 1 cup warm water, 1/3 cup vegetable oil, and 1 1/2 teaspoons vanilla extract. Use a hand mixer to beat on medium speed until the batter is smooth and lump-free. Pour the batter evenly onto the prepared baking sheet.
Bake for 30–35 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow the cake to cool completely in the pan.
Coconut Pecan Frosting
In a medium saucepan, melt 1/2 cup salted butter over medium heat. Whisk in 1/2 cup granulated sugar and 1/2 cup brown sugar until combined.
Whisk in 3 large egg yolks, 1 (12 ounce can) evaporated milk, and 2 teaspoons vanilla extract. Cook the mixture over medium heat for 12–14 minutes, stirring frequently, until it thickens and coats the back of a spoon.
Remove from heat and stir in 1 1/2 cups unsweetened coconut flakes and 1 cup chopped pecans. Allow the filling to cool completely before spreading it evenly over the cooled cake.