Preheat your oven to 350°F (175°C) and grease or line a muffin tin with paper liners.

In a large mixing bowl, whisk together the flour, baking powder, cinnamon, nutmeg, and salt until well combined. This ensures even distribution of the leavening agent and spices.

In another bowl, combine the pumpkin puree, granulated sugar, brown sugar, milk, melted butter, and eggs. Whisk until smooth and well incorporated.

Gradually add the wet ingredients to the dry ingredients, folding gently with a spatula until just combined. Be careful not to overmix, as this can lead to dense muffins.

In a small bowl, mix the brown sugar and cinnamon for the swirl. Set aside.

Spoon half of the muffin batter into the prepared muffin tin, filling each cup about halfway.

Sprinkle a teaspoon of the cinnamon sugar mixture over the batter in each cup, then top with the remaining muffin batter, filling each cup nearly to the top.

Using a toothpick or a knife, gently swirl the batter to incorporate the cinnamon mixture without fully mixing it in.

Bake in the preheated oven for 18-20 minutes, or until a toothpick inserted into the center comes out clean. The muffins should be lightly golden on top.

Allow the muffins to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.

In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth. Adjust the milk quantity for your desired glaze consistency.

Drizzle the glaze over the cooled muffins before serving for a sweet finish.