Preheat the oven to 425°F (220°C). Line all 12 cups of a standard muffin pan with paper liners. Lightly grease the liners if they are not labeled nonstick.

In a small bowl, stir together the brown sugar, flour, and cinnamon. Add the melted butter and mix until the filling resembles thick, damp crumbs. Set it aside while preparing the batter.

In a medium bowl, whisk together the flour, baking soda, baking powder, cinnamon, ginger, nutmeg, and salt. Break up any compacted flour and make sure the spices and leavening are evenly distributed.

In a large bowl, whisk the pumpkin puree and brown sugar until smooth. Add the eggs, oil, milk, and vanilla, then whisk until the mixture looks glossy and evenly blended.

Add the dry ingredients to the pumpkin mixture: Fold gently with a flexible spatula until no dry flour remains. The batter should be thick, smooth, and scoopable rather than pourable. Stop mixing as soon as it is uniform.

Spoon approximately 1 1/2 tablespoons of batter into each prepared muffin cup. Spread it gently so the bottom of each liner is covered.

Sprinkle approximately half of the cinnamon filling evenly among the muffin cups. Keep most of the filling near the center so melted sugar does not stick to the edges of the pan.

Divide the remaining pumpkin batter among the muffin cups. Sprinkle the remaining cinnamon filling over the tops.

Insert a butter knife or thin skewer into each muffin and make one or two shallow circular motions. Do not stir deeply or repeatedly, as excessive swirling can blend the filling into the batter and create gummy pockets.

Bake the muffins at 425°F (220°C) for 5 minutes. Without opening the oven door, reduce the temperature to 350°F (175°C).

Continue baking for 16 to 19 minutes. The muffins are done when the tops are rounded and set, the centers spring back lightly, and a toothpick inserted away from a cinnamon ribbon comes out clean or with a few moist crumbs.

If wet pumpkin batter clings to the toothpick, continue baking for 2 minutes before checking again. If the tops become too dark, place a loose sheet of aluminum foil over the pan.

Place the pan on a wire rack and let the muffins cool for 10 minutes. Transfer them from the pan to the rack and cool for another 10 minutes before glazing.

Whisk the powdered sugar, milk, vanilla, and salt in a small bowl until smooth. The glaze should fall from the whisk in a thick ribbon. Add additional milk 1 teaspoon (5 ml) at a time only if it is too thick to drizzle.

Drizzle the glaze over the cooled muffins: Let them stand for 5 minutes, or until the glaze begins to set, before serving.