Preheat your oven to 375°F (190°C). Line a muffin tin with paper liners.
In a large bowl, whisk together the flour, sugar, baking powder, and salt.
In a separate bowl, whisk together the pumpkin puree, milk, vegetable oil, egg, and vanilla extract.
Add the wet ingredients to the dry ingredients and mix until just combined. Do not overmix.
In a small bowl, combine the brown sugar, cinnamon, and softened butter. Mix until well combined.
Fill each muffin cup about halfway with the batter. Spoon a teaspoon of the cinnamon-sugar mixture on top of the batter in each cup. Swirl with a knife or toothpick.
Bake for 20-25 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.
Let the muffins cool in the muffin tin for a few minutes before transferring them to a wire rack to cool completely.
While the muffins are cooling, prepare the frosting. In a medium bowl, beat together the cream cheese and powdered sugar until smooth and creamy.
Frost the cooled muffins with the cream cheese frosting. Serve immediately.
