Preheat the oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
In a large mixing bowl, sift together the flour, cocoa powder, sugar, baking powder, baking soda, and salt.
Add the eggs, milk, vegetable oil, and 2 teaspoons vanilla extract to the dry ingredients. Beat on medium speed for 2 minutes until well combined.
Stir in the boiling water carefully. The batter will be thin; this is normal.
Divide the batter evenly between the prepared cake pans.
Bake for 30 to 35 minutes or until a toothpick inserted into the center comes out clean.
Remove the cakes from the oven and allow them to cool in the pans for 10 minutes. Then, turn them out onto wire racks to cool completely.
To make the vanilla frosting, beat the softened butter on medium speed until creamy, about 2 minutes.
Gradually add the powdered sugar, 1 cup at a time, beating on low speed until incorporated.
Add the milk, vanilla extract, and salt. Beat on high speed for 3 minutes until the frosting is light and fluffy.
Once the cakes are completely cool, place one layer on a serving plate. Spread a layer of vanilla frosting over the top.
Place the second cake layer on top and frost the top and sides of the cake evenly.
Slice and serve. Store any leftovers covered at room temperature for up to 2 days or refrigerated for up to 5 days.