Preheat your oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners for easy cleanup.

In a large bowl, whisk together the all-purpose flour, granulated sugar, baking powder, and salt.

In a separate bowl, whisk together the milk, melted butter, egg, and vanilla extract until well combined.

Pour the wet ingredients into the dry ingredients, mixing gently until just combined. Do not overmix, as that can make the muffins tough.

In a small bowl, combine the brown sugar, ground cinnamon, and softened butter to make a thick, spreadable filling.

Fill each muffin cup halfway with the muffin batter. Spoon a generous dollop of the cinnamon-sugar mixture on top of each, gently swirling with a toothpick or knife. Add the remaining muffin batter to fill each cup about ¾ full, then swirl a bit more of the cinnamon mixture on top.

Bake the muffins for 18–20 minutes, or until a toothpick inserted into the center comes out clean.

Let the muffins cool in the pan for 5 minutes, then transfer to a wire rack to cool completely before glazing.

In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth and pourable.

Drizzle the glaze generously over the cooled muffins. Allow the glaze to set for a few minutes before serving.