The original recipe for these muffins call them "doughnut muffins" -- that is, just like doughnuts only baked in a muffin tin. While delicious, these are not nearly as dense as a doughnut. (For muffins that really do taste like doughnuts, try this Pumpkin Ice Cream Muffin recipe.) I confess, I made quite a few modifications, so perhaps that's the culprit.
Generally, I followed the directions as given (except I ended up cooking all the liquid out of the apples. Oops.) The original recipe doesn't tell when to add them to the batter; I made sure they were cool enough not to cook the egg, then added them slowly to the wet mixture. I then gently stirred in the combined dry ingredients. I baked them for 23 minutes, but you should start checking them after 15 minutes. While still warm, I spread a little melted butter on the tops and then dunked the tops into cinnamon sugar.
Conclusion: These were a little fussy with all the ingredients and the extra step of cooking down the apples, but they were really tasty. Not at all doughnut-like, but soft and light -- the perfect muffin texture. I highly recommend a tart apple, because it gives a wonderful tang that contrasts nicely with all the spices and the sweet cinnamon-sugar topping.
Original recipe: Mini Apple Cider Doughnut Muffins via Fia's Maine Kitchen