Step 1: Preheat oven to 400°F (200°C). Line a 12-cup muffin pan with paper liners or grease well.
Step 2: In a large bowl, whisk together flour, granulated sugar, ½ cup brown sugar, baking powder, baking soda, cinnamon, ginger, nutmeg, cloves, and salt.
Step 3: In a separate medium bowl, whisk together egg, pumpkin puree, buttermilk, melted butter, and vanilla extract until smooth.
Step 4: Pour the wet ingredients into the dry ingredients. Mix with a spatula or spoon until just combined. Do not overmix; a few lumps are okay.
Step 5: Spoon half of the muffin batter evenly into the prepared muffin cups.
Step 6: For the Cinnamon Swirl: In a small bowl, combine 2 tbsp melted butter, ¼ cup brown sugar, and 1 tbsp cinnamon. Mix until a thick paste forms.
Step 7: Dollop about ½ teaspoon of the cinnamon swirl mixture over the batter in each muffin cup. Use a toothpick or small knife to gently swirl it into the batter.
Step 8: Top with the remaining muffin batter, dividing evenly among the cups.
Step 9: Dollop the remaining cinnamon swirl mixture on top of each muffin and swirl again lightly.
Step 10: Bake for 5 minutes at 400°F (200°C), then reduce oven temperature to 375°F (190°C) and bake for another 13-17 minutes, or until a toothpick inserted into the center of a muffin comes out clean or with a few moist crumbs.
Step 11: Remove from oven and let cool in the muffin pan for 5 minutes before transferring to a wire rack to cool completely.
Step 12: For the Cream Cheese Glaze: While muffins cool, in a medium bowl, beat softened cream cheese and softened butter with an electric mixer until light and fluffy.
Step 13: Gradually add powdered sugar, beating until smooth.
Step 14: Beat in milk/cream and vanilla extract until the glaze reaches a smooth, pourable consistency. Add more milk if needed for a thinner glaze.
Step 15: Once muffins are completely cool, drizzle or spread the cream cheese glaze generously over each muffin.