In another mixing bowl, combine the oil with the sugar, milk, sour cream, vanilla and eggs. Whisk everything together until it's a smooth mixture, about 1 minute.
In a small bowl, combine the butter, brown sugar and remaining 1/2 teaspoon of cinnamon and rub it together with your fingertips until it's crumbly. Set aside.
Fill each paper cup about 3/4 of the way up with the batter and then sprinkle each one with the brown sugar mixture, dividing it evenly among the muffins.
Bake in the preheated 375°F oven until they no longer look wet and a wooden toothpick inserted into the center of a muffin comes out clean, about 20 minutes.