Preheat oven to 400 degrees and grease a 6-count donut pan liberally with baking spray.
In a large bowl, sift flour, sugar, brown sugar, baking powder, nutmeg, and salt together.
In a second bowl, whisk egg, buttermilk, sour cream, and vanilla extract together.
Make a well in the center of the dry ingredients and add in the wet ingredients. Gently mix the batter until combined.
Add in melted butter and apples and mix until combined.
Spoon the batter into the donut pan, evenly distributing the batter between the 6 donut cavities (you may have enough batter to make 7-8 donuts).
Bake for 10-12 minutes, or until the donuts are lightly golden and 'spring' back when touched.
Allow to cool for 10-15 minutes.