Preheat the oven to 350 degrees Fahrenheit so it can heat up while you prepare the batter.
Line a muffin tin with paper liners and set it aside.
In a large bowl, whisk together the butter, oil, pumpkin puree, and eggs until everything is well combined.
Add the eggs, both the granulated sugar and brown sugar, and vanilla extract. Mix until everything is fully incorporated.
Stir in the flour, pumpkin pie spice, baking soda, and salt. Mix until just combined and there are no dry spots.
Gently fold in the mashed banana until it is evenly distributed throughout the batter.
Divide the batter evenly among the prepared muffin cups, filling each one about 3/4 full.
Place the muffin tin in the preheated oven and bake for 18-20 minutes.
To check if they are done, insert a toothpick into the center of a muffin. If it comes out clean or with just a few crumbs, the muffins are ready.
Allow the muffins to cool in the tin for a few minutes, then transfer them to a wire rack to cool completely. Enjoy your delicious Pumpkin Banana Bread Muffins!