Name: Doberge Cake (Dobash)
Prep time: 40 min
Cook time: 10 min
Total time: 50 min
Yield: 10
Ingredients: 1 (15.25 ounce) package white cake mix (such as Duncan Hines); 1 tablespoon all-purpose flour; 1 tablespoon white sugar; 1 teaspoon baking powder; 1 ⅓ 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; ¼ cup unsalted butter, softened; 1 (16 ounce) box confectioners' sugar; ½ cup unsweetened cocoa powder; ½ teaspoon vanilla extract; 1 tablespoon milk, or as needed