Preheat oven to 400°F. Line a 12-cup muffin pan with liners.
Make the streusel by mixing the brown sugar, granulated sugar, and cinnamon. Stir in melted butter, then gently mix in the flour with a fork until large crumbs form. Set aside.
In a large bowl, whisk together flour, granulated sugar, brown sugar, pumpkin pie spice, salt, baking soda, and baking powder.
In a separate bowl, whisk together eggs, pumpkin puree, vegetable oil, and vanilla.
Pour the wet ingredients into the dry ingredients and gently fold until just combined. Don't overmix.
Divide the batter among the muffin cups, filling them about ¾ to ⅞ full.
Sprinkle the streusel generously over the muffin batter.
Bake at 400°F for 5 minutes. Without opening the oven, reduce the temperature to 350°F and bake for another 15–18 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.
Cool in the pan for 5 minutes, then transfer to a wire rack.