1. Place a rack in the center of the oven and preheat the oven to 350 degrees. Lightly mist two 9-inch round cake pans with vegetable oil spray, then dust them with the rice flour. Shake out the excess rice flour and set the pans aside.
2. Place the cake mix, pudding mix, milk, butter, eggs, and vanilla in a large mixing bowl and beat with an electric mixer on low speed until the ingredients are just incorporated, 30 seconds. Stop the machine and scrape down the side of the bowl with a rubber spatula. Increase the mixer speed to medium and beat the batter until smooth, 1 to 1 1/2 minutes longer, scraping down the side of the bowl again if needed. The batter should look well blended. Divide batter evenly between the 2 prepared cake pans, smoothing the tops with the rubber spatula. Place the pans in the oven side by side.
3. Bake the cake layers until they are golden brown and the tops spring back when lightly pressed with a finger, 19 to 23 minutes. Transfer the cake pans to wire racks and let the cake layers cool for 5 minutes. Run a sharp knife around the edge of each layer and give the pans a good shake to loosen the cakes. Invert each layer on a wire rack, then invert again onto another rack so that the layers are right side up. Let the layers cool completely, about 20 minutes longer.
4. Meanwhile, make the Chocolate Buttercream Frosting (recipe below).
5. To assemble the cake, transfer one layer, right side up, to serving plate. Spread the top with about 1 cup of the frosting. Place the second cake layer, right side up, on top of the first layer and frost the top and sides of the cake, working with smooth, clean strokes.