Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9x13-inch baking dish.
Beat sugar, cocoa powder, and shortening together in a large bowl with an electric mixer until light and fluffy. Beat in 1 egg at a time until smooth. Sift 2 cups flour, baking soda, and salt together in a separate bowl. Add portions of flour mixture and milk alternately, beating well after each addition. Stir in boiling water and vanilla extract to form a thin batter. Pour batter into prepared baking dish.
Bake in preheated oven until a toothpick inserted into the center comes out clean, about 30 minutes. Cool in the baking dish for 10 minutes before removing to cool completely on a wire rack.