Step 1: Preheat your oven to 350°F (175°C) and generously grease a doughnut pan with non-stick spray or butter.
Step 2: In a large mixing bowl, whisk together the flour, granulated sugar, brown sugar, baking powder, cinnamon, nutmeg, and salt until well combined.
Step 3: In a separate medium bowl, whisk together the sweet potato puree, eggs, melted butter, 1/4 cup maple syrup, and vanilla extract until smooth.
Step 4: Gently fold the wet ingredients into the dry ingredients using a spatula, stirring just until no streaks of flour remain.
Step 5: Transfer the batter to a piping bag and fill each doughnut cavity about 3/4 full.
Step 6: Bake for 12-15 minutes, or until the doughnuts are golden and a toothpick inserted comes out clean.
Step 7: Allow the doughnuts to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.
Step 8: Prepare the glaze by whisking together the powdered sugar, 3 tbsp maple syrup, and milk in a small bowl until smooth.
Step 9: Dip the tops of the cooled doughnuts into the glaze and place them back on the wire rack to set.