Heat the oven to 375°F. Line a 12-cup muffin pan with paper liners, or grease it well.
For the cinnamon sugar topping, stir the sugar and cinnamon together in a small bowl before you mix the batter.
For the streusel, rub the cold butter into the flour, brown sugar, and cinnamon with your fingertips until it looks like damp sand with a few pea-size lumps.
In a medium bowl, whisk the flour, baking soda, baking powder, cinnamon, nutmeg, ginger, and salt.
In a large bowl, whisk the pumpkin, brown sugar, oil, eggs, milk, and vanilla until smooth.
Pour the dry ingredients into the wet ones. Fold gently with a spatula until no dry streaks remain.
Divide the batter evenly among the 12 cups. The cups will look nearly full.
Sprinkle the cinnamon sugar generously over each cup, or crumble the streusel over the batter and press lightly so it sticks.
Bake for 20 to 24 minutes, until a toothpick in the center comes out clean. Keep the oven door closed for the first 15 minutes.
Cool the muffins in the pan for 5 minutes. Then move them to a wire rack.
For the glaze, stir the powdered sugar, milk, and cinnamon together. Drizzle it over the muffins only after they cool completely.