Name: Doberge Cake (Dobash)
Ingredients: 1 (18.25 ounce) package white cake mix (such as Duncan Hines®); 1 tablespoon all-purpose flour; 1 tablespoon white sugar; 1 teaspoon baking powder; 1 1/3 cups water; 3 egg whites; 2 tablespoons vegetable oil; 2 cups milk; 1 (3.9 ounce) package instant chocolate pudding mix; 1 (4 ounce) package cream cheese, softened; 0.25 cup butter, softened; 1 (16 ounce) box confectioners' sugar; 0.5 cup unsweetened cocoa powder; 0.5 teaspoon vanilla extract; 1 tablespoon milk, or as needed

Ingredients

1 (18.25 ounce) package white cake mix (such as Duncan Hines®)
1 tablespoon all-purpose flour
1 tablespoon white sugar
1 teaspoon baking powder
1 1/3 cups water
3 egg whites
2 tablespoons vegetable oil
2 cups milk
1 (3.9 ounce) package instant chocolate pudding mix
1 (4 ounce) package cream cheese, softened
0.25 cup butter, softened
1 (16 ounce) box confectioners' sugar
0.5 cup unsweetened cocoa powder
0.5 teaspoon vanilla extract
1 tablespoon milk, or as needed

Steps

Preheat the oven to 350 degrees F (175 degrees C). Grease and flour 5 (8-inch) round cake pans; line with parchment paper.
Whisk cake mix, flour, sugar, and baking powder together in a large mixing bowl. Add water, egg whites, and vegetable oil; beat with an electric mixer on low speed until thoroughly mixed. Increase speed to medium and beat for 2 minutes. Pour 1 cup batter into each of the 5 prepared cake pans.
Bake in the preheated oven until cakes are set in the middle, about 8 minutes. Watch carefully so the thin cakes don't burn. Cool in pans for 10 minutes, then turn cakes out onto wire racks to finish cooling.
Whisk 2 cups milk and pudding mix together in a bowl until combined; let stand 2 minutes to thicken. Place 1 cake layer on a serving plate; spread about 1/2 cup pudding on top. Stack 1 cake layer on top; repeat with remaining pudding and cake layers, ending with cake layer.
Mash cream cheese and butter together in a bowl until thoroughly combined; mix in confectioners' sugar, cocoa powder, vanilla extract, and milk, slowly adding and mixing in milk to reach a spreadable frosting consistency. Frost top and sides of cake. Refrigerate leftovers.