Preheat oven to 350°F. Grease an 8-inch or 9-inch square or round cake pan or line with parchment. Set aside.
In a large mixing bowl, whisk together the flour, sugar, baking soda, baking powder, and salt. Make a well in the center and add the egg, oil, and buttermilk. Whisk to combine.
Add the hot water and whisk again until smooth. Add the vanilla extract; whisk to combine. At this point you should have a very thin, smooth batter.
Pour the batter into the prepared pan. Tap the pan gently on the counter a few times to release any big air bubbles. Bake for 25-30 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Let the cake cool completely before frosting.
FOR THE FROSTING:
In a large bowl, beat the butter, buttermilk (or cream), and vanilla extract with an electric mixer on medium-high speed until smooth, about 1 minute. Reduce the speed to medium-low, and gradually add the powdered sugar. Beat until smooth, about 4 minutes. Increase the speed to medium-high and beat until the frosting is light and fluffy, about 4 more minutes.
Spread the frosting on the cooled cake. Garnish with sprinkles, if desired.
Notes
For a larger cake, double all of the ingredients and bake the cake in a 13 x 9-inch pan. Bake for 30-35 minutes.
For a layer cake, double all of the ingredients, and divide the batter evenly between two 8-inch or 9-inch round cake pans.
This recipe yields enough frosting for the top of an 8-inch or 9-inch cake. If you'd like to frost the sides of the cake as well, or if you want to bake a larger cake, you'll need to double the frosting ingredients.
Use sprinkles for any occasion -- rainbow sprinkles for a birthday, red and blue for July 4th, red and green for Christmas, and so on. It's a festive cake at every celebration!
Fold rainbow sprinkles into the batter for a funfetti cake.
Line the cake pan with parchment, allowing some of the parchment paper to hang over the sides, if you'd like to be able to lift the cake out of the pan before frosting and slicing.
Use thick, full-fat buttermilk. This adds richness, moisture, and flavor to the cake that you don't get with low-fat varieties.
Make sure that all of your ingredients are at room temperature. This helps them blend together more easily and smoothly, and helps to avoid over-mixing (which can result in a dry, dense cake).
Do not over-bake the cake or it can become dry. Start checking for doneness by the 25-minute mark, since total baking times will vary depending on your personal oven and the pans that you use.