Preheat your oven to 350°F and line a muffin pan with 10 muffin liners.
In a large bowl, whisk together the flour, cornmeal, baking powder, and salt.
In a separate bowl, whisk together the melted butter, oil, sugar, milk, and eggs until well combined.
Add the wet ingredients to the dry ingredients and mix just until combined. Don't overmix.
Divide the batter evenly among the 10 prepared muffin cups.
In a small bowl, mix the softened cream cheese, sugar, and flour until smooth.
Using a mini cookie scoop, add a scoop of the cream cheese mixture directly on top of each muffin.
Bake for 13–14 minutes at 350°F, or until the muffins are set and a toothpick inserted into the cornbread portion comes out clean. A few crumbs are fine. Don't overbake!
Allow the muffins to cool in the pan for a few minutes before transferring them to a wire rack. Serve warm with honey and enjoy!