Preheat oven to 375°F and line a 12-cup muffin tin with paper liners.

Whisk 2 cups flour, 1/2 cup sugar, 2 teaspoons baking powder, and 1/2 teaspoon salt in a large bowl.

Whisk 1/4 cup of the melted butter, 3/4 cup milk, the egg, and 1 teaspoon vanilla in a separate bowl, then stir into the dry ingredients until just combined.

Mix the brown sugar, cinnamon, and remaining 1/4 cup melted butter in a small bowl to make the swirl filling.

Divide half the muffin batter among the liners, then drop a teaspoon of the cinnamon filling onto each and swirl gently with a toothpick.

Top with the remaining batter and swirl a little more filling across the tops.

Bake for 18 to 20 minutes, until a toothpick inserted in the center comes out clean.

Cool muffins in the tin for 5 minutes, then transfer to a wire rack to cool for 15 minutes more.

Whisk the powdered sugar with 2 to 3 tablespoons milk until the glaze drizzles in a thin ribbon off the whisk.

Drizzle glaze over the muffins and let it set for 10 minutes, until no longer wet to the touch.

Package muffins in their paper liners inside a bakery box or stacked in a clear clamshell container, one layer deep so the glaze does not stick to the lid.