01 - Preheat oven to 350°F. Line a 12-cup muffin tin with paper liners or grease each cup thoroughly.
02 - Whisk together all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg in a large mixing bowl.
03 - In a separate mixing bowl, blend the pumpkin purée, granulated sugar, brown sugar, eggs, melted butter, milk, and vanilla extract until the mixture is smooth.
04 - Pour wet ingredients into dry ingredients and gently stir just until combined. Avoid overmixing for best texture.
05 - Fold in grated sharp cheddar cheese evenly throughout the batter.
06 - Divide the batter equally among the prepared muffin cups, filling each about three-quarters full.
07 - Bake for 20 to 22 minutes or until a toothpick inserted into the center of a muffin comes out clean.
08 - Allow muffins to cool in the pan for 5 minutes, then transfer each to a wire rack.
09 - While muffins are still warm, brush the tops of each muffin with melted butter.
10 - Combine granulated sugar and ground cinnamon in a small bowl. Dip or sprinkle each muffin top generously with this mixture.
11 - Serve muffins warm or at room temperature.