Preheat your oven to 375F. Line 12 muffin tins with paper liners or spray them with nonstick cooking spray.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the melted butter and brown sugar until they are combined and have the consistency of caramel— about 3 minutes on medium-high speed.
Next, add the vegetable oil, eggs, and vanilla extract. Mix on low speed until they are fully combined.
Next, in a small bowl, combine the flour and baking powder.
With the mixer on low, alternate by adding 1/3 of the dry ingredients. Next, add ½ of the milk. Now add another ⅓ of the dry ingredients. Then, add the remaining milk followed by the remaining flour. Mix just until no large lumps remain. Use a silicone spatula to scrape down the sides of the bowl and make sure no sugar is left at the bottom.
Divide the batter evenly between the muffin pans; filling each one about ¾ of the way full. I use a ¼ cup cookie scoop to ensure all of the muffins are the same size.
Bake the muffins in a preheated oven for 15-18 minutes, or until they are lightly browned and the toothpick test is clean.