Preheat the oven to 350 degrees F (175 degrees C). Coat a 12-cup muffin tin with nonstick spray.
Puree avocado flesh in a food processor or blender. Transfer to a large bowl and mix in pumpkin puree, sugar, and vanilla.
Sift in flour, pumpkin pie spice, baking powder, and salt; beat until well combined. Spoon batter into the prepared muffin cups, filling each 3/4 full.
Bake in the preheated oven until tops spring back when lightly pressed, 20 to 25 minutes. Cool in the tin for 5 minutes. Transfer to a wire rack to cool completely.