Prep the oven and pan: Heat oven to 425°F (220°C). Line a 12-cup muffin pan with paper liners or grease well.
Make the streusel: In a small bowl, mix 1/2 cup all-purpose flour, 1/3 cup brown sugar, 1 teaspoon pumpkin pie spice, and a pinch of salt.
Cut in 1/4 cup cold unsalted butter (cubed) until crumbly. Chill while you make the batter.
Whisk dry ingredients: In a large bowl, whisk 2 cups all-purpose flour, 1 tablespoon baking powder, 1/2 teaspoon baking soda, 1/2 teaspoon salt, and 2 teaspoons pumpkin pie spice.
Combine wet ingredients: In another bowl, whisk 1 cup canned pumpkin puree, 2/3 cup brown sugar, 1/3 cup granulated sugar, 2 large eggs, 1/3 cup vegetable oil, 2 tablespoons melted butter (cooled), 1/2 cup milk, and 2 teaspoons vanilla.
Mix the batter: Pour wet ingredients into dry. Stir gently until just combined.
It should be thick and a little lumpy. Do not overmix.
Fill and top: Divide batter evenly among the muffin cups, filling each about 3/4 full. Sprinkle a generous layer of streusel over each muffin, pressing lightly so it sticks.
Bake high, then lower: Bake at 425°F for 5 minutes. Without opening the oven, lower the temperature to 350°F (175°C) and bake 13–16 more minutes, until a toothpick comes out clean or with a few moist crumbs.
Cool: Let muffins cool in the pan 5 minutes, then transfer to a rack.
Optional glaze: Stir 1/2 cup powdered sugar with 1–2 teaspoons milk and a drop of vanilla until smooth.
Drizzle over cooled muffins.