Preheat oven to 375F and line a 12-cup muffin tin with paper liners. In a large bowl, whisk together gluten free flour, brown sugar, pumpkin pie spice, baking soda, baking powder, and salt.
In a separate bowl, whisk together pumpkin puree, vegetable oil, eggs, milk, and vanilla extract until smooth. Pour the wet ingredients into the dry ingredients and stir until just combined.
Make the streusel by combining gluten free flour, brown sugar, and cinnamon. Rub in the cold butter with your fingertips until crumbly.
Divide batter evenly among the muffin cups, filling about three-quarters full. Sprinkle the streusel generously over the top of each muffin.
Bake for 20 to 22 minutes until a toothpick inserted in the center comes out clean. Cool in the pan for 5 minutes, then transfer to a wire rack. Serve warm or at room temperature.