Preheat oven to 350°F. Stir together all wet ingredients needed to prepare cake and brownie batters (per package directions) in 1 large bowl. Stir together dry ingredients from cake and brownie mix packages in a separate bowl. Add dry ingredients to wet ingredients, and stir together until well blended. Pour combined batter into a greased and floured 12-cup Bundt pan. Bake until a wooden pick inserted in center comes out clean, 50 to 55 minutes. Cool cake in pan on a wire rack 30 minutes. Invert onto rack, and cool completely, about 1 hour.

Place chopped milk chocolate and bittersweet chocolate in a medium-size microwavable bowl. Microwave on HIGH until melted and smooth, about 1 minute, stirring after 30 seconds. Cool 5 minutes.

Place butter in bowl of a heavy-duty stand mixer fitted with the paddle attachment. Beat on medium speed until creamy, 1 to 2 minutes. Reduce speed to low; gradually add powdered sugar and cocoa, beating until smooth, about 1 minute, stopping to scrape sides of bowl as needed. Beat in sour cream and vanilla; gradually beat in cooled melted chocolate. Increase speed to medium; beat until smooth, 2 to 3 minutes.

Spoon mixture into a piping bag fitted with a 1⁄4-inch round tip; pipe frosting onto the top of the cooled cake in a decorative pattern. Press edible flowers onto frosting to decorate cake as desired.