@Anonycat
Preheat the oven to 350F.
Mix 1/4 cup softened (not melted!) butter and 3/4 cup sugar with an electric mixer until fluffy, then add an egg and blend that. Add half a teaspoon of vanilla and 8 oz of sour cream and blend that, add 1 1/4 cups of AP flour, half a tsp of baking powder and 1/4 tsp baking soda and mix that until just combined.
Grab an 8” x 8” aluminum cake pan, cover the bottom with half of the batter, slather a layer of Nutella on top and then top that with the rest of the batter. You don’t have to use a disposable pan, but if you don’t you probably need to grease it first.
I originally set the timer at half an hour, but that was way too short. I kept checking the cake until it was golden brown. I think it wound up taking 45-50 minutes.
Do the skewer test to make sure it’s cooked all the way through and let it cool on a rack.
For the frosting I creamed together a cup of softened unsalted butter and 3 1/2 cups of powdered sugar, half a cup at a time.
After each cup of sugar was added, I added half a cup of Nutella, 1 tablespoon at a time. Then I added a tablespoon of vanilla and then beat it on high for about 20 seconds to lighten the frosting.
After this I added two tablespoons of whole milk, one tablespoon at a time until the buttercream would hold its shape. Added pinch of salt and whipped on high for a final 20 seconds.
This yielded way too much frosting for that one cake, though. Wound up baking other things to use it all. You could probably get away with halving all ingredients.