Mix the melted butter, brown sugar, and cinnamon for the swirl. Place in a piping bag and let sit at room temperature to thicken slightly.
Preheat oven to 375°F (190°C). Whisk together flour, granulated sugar, baking powder, and salt in a large bowl.
In a separate bowl, whisk milk, eggs, melted butter, and vanilla. Gently fold wet ingredients into dry ingredients until just combined.
Melt 1 tablespoon of butter in a 10-inch or 12-inch cast-iron skillet over medium-low heat on the stove.
Pour batter into the hot skillet. Instantly pipe the cinnamon mixture in a swirl pattern over the batter, starting from the center outwards.
Transfer skillet to the oven and bake for 15-18 minutes until puffed and the center is set.
While baking, beat cream cheese and butter until smooth. Add powdered sugar, vanilla, and milk until you reach a pourable glaze consistency.
Remove skillet from oven, let rest for 5 minutes, drizzle heavily with the glaze, slice, and serve warm.