To make the cake, combine the flour, sugar, cocoa powder, baking powder, baking soda, and salt in a bowl. Whisk to combine.
Add the eggs, milk, and vanilla and mix with an electric mixer for about 2 minutes. Carefully add the boiling water and mix until combined.
Pour the batter into a greased and floured 13x9-inch baking pan. Bake in a preheated 350-degree F oven for about 35 to 40 minutes. Cool slightly then invert onto a serving platter. Cool completely.
To make the frosting, combine the butter, lemon juice, vanilla, and powdered sugar. Beat until fluffy. Add the yellow food coloring to achieve the desired color, if using. (Add more powdered sugar, if needed, to get the right frosting consistency.)
Frost the cooled cake.
