Step 1: Preheat your oven to 350°F (175°C) and generously grease two 6-cavity doughnut pans with non-stick spray or butter.
Step 2: In a large mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt until well combined.
Step 3: In a medium bowl, whisk the egg with the granulated sugar and brown sugar until smooth. Add the milk, sour cream, melted butter, and vanilla extract, whisking until fully incorporated.
Step 4: Pour the wet ingredients into the dry ingredients and stir with a spatula until just combined. Fold in the grated apple gently.
Step 5: Transfer the batter to a piping bag and pipe into the prepared doughnut pans, filling each cavity about 3/4 full.
Step 6: Bake for 10-12 minutes, or until a toothpick inserted into the center comes out clean. Let the doughnuts cool in the pan for 5 minutes before transferring to a wire rack.
Step 7: To make the glaze, whisk together powdered sugar, maple syrup, and enough milk to reach a thick, dipping consistency.
Step 8: Dip the tops of the slightly warm doughnuts into the glaze and set back on the rack to allow the glaze to harden.