Preheat oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or spray with cooking spray.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt.
In a large bowl, combine melted butter (cooled), oil, and sugar. Whisk in eggs one at a time, then stir in vanilla.
Add dry ingredients in three parts, alternating with buttermilk. Mix gently until just combined.
For the filling, combine brown sugar, cinnamon, and melted butter. Stir until it resembles wet sand.
Fill each muffin cup halfway with batter, add a heaping teaspoon of cinnamon filling, and top with remaining batter. Swirl with a toothpick 2-3 times.
Bake for 18-20 minutes until golden brown and a toothpick comes out clean.
For the glaze, beat cream cheese and butter until smooth. Add powdered sugar, milk, and vanilla. If too thick, add more milk.
Cool muffins for 5 minutes, then drizzle with glaze when warm. Enjoy!