Heat the oven to 350° and grease the bottom only of 12 muffin cups.
In a large bowl, combine the pumpkin, oil, eggs, vanilla, and brown sugar. In a medium bowl, whisk together the flour, pumpkin pie spice, baking powder, baking soda, and salt. Add the flour mixture to the pumpkin mix, stirring until just combined.
Pour the batter into the muffin cups and bake until the muffins are slightly puffed and golden brown, about 25 minutes. Cool in the pan on a wire rack.