I think the secret to the flavor connection is the nutmeg in the batter which I'm fairly certain is common in cake doughnuts.
Muffins That Taste Like Doughnuts
adapted from lemanada on Tasty Kitchen
1 3/4 c. flour
1 1/2 tsp. baking powder
1/2 tsp. salt
1/2 tsp. nutmeg
1/2 tsp. cinnamon
1/3 c. oil
3/4 c. white sugar
1 whole egg
3/4 c. milk
1/4 c. butter
1/3 c. white sugar
1 Tbsp. cinnamon
Combine flour, baking powder, salt, nutmeg and cinnamon.
Combine oil, sugar, egg and milk. Add dry ingredients and stir only to combine. Spoon into well-greased muffin tins (silicone pans work well).
Bake at 350 degrees for 15-20 minutes. Meanwhile, melt the butter in a bowl. Combine the white sugar with the cinnamon in another bowl.
Shake muffins out while still hot. Dip muffins in butter, then into the sugar/cinnamon mix. Let cool.