Preheat your oven to 350°F (175°C) and line a muffin tin with paper liners or grease it lightly.
In a large bowl, whisk together the flour, granulated sugar, baking powder, salt, and ground cinnamon.
In another bowl, combine the melted butter, egg, milk, and vanilla extract. Mix well.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix.
In a small bowl, mix together the brown sugar, ground cinnamon, and softened butter to create the cinnamon swirl mixture.
Fill each muffin cup about halfway with the batter. Add a spoonful of the cinnamon swirl mixture on top of the batter, then cover with more batter until the cups are about 3/4 full.
Use a toothpick or a knife to gently swirl the cinnamon mixture into the batter.
Bake for 18-20 minutes, or until a toothpick inserted into the center comes out clean.
While the muffins are baking, prepare the glaze by whisking together the powdered sugar, milk, and vanilla extract in a small bowl until smooth.
Once the muffins are done, allow them to cool in the pan for 5 minutes before transferring them to a wire rack. Drizzle the glaze over the warm muffins.