Preheat the oven to 350F degrees and spray a doughnut pan with non-stick cooking spray. You'll end up with about 6-8 doughnuts total, so you may need to bake them in 2 batches or use 2 doughnut pans. 

In a separate medium-sized bowl whisk together the melted butter, egg, vanilla, sour cream and buttermilk. Ensure all the wet ingredients are room temperature before mixing them together. Otherwise the butter will form clumps and the mixture won't be useable. Then whisk in the food coloring and distilled vinegar. 

Add the wet ingredients into the dry ingredients and whisk until just combined. Be very careful to only mix the batter until they're just combined. Spoon the batter into a large ziplock bag, cut the bottom corner off so there's about ½ inch opening in the bottom corner. Then pipe the batter into the prepared doughnut pan. Or spoon the batter into the doughnut pan. Each doughnut cavity should be about ⅔s and you'll end up with about 6-8 doughnuts total.

Bake in the preheated oven for 8-10 minutes or until the doughnuts feel slightly firm to the touch. Allow to cool for 5 minutes in the pan, then continue cooling on a wire rack. 

In a medium sized bowl whisk or stir together the butter and cream cheese until combined. Add in 1 cup powdered sugar and 1 tablespoon of cream or milk and whisk until combined. Add in more powdered sugar and cream until the desired sweetness level is reached. The consistency should thinner than peanut butter.