Activate yeast: In a large bowl, combine warm milk, yeast, and 1 tablespoon of the granulated sugar. Let stand for 5-10 minutes until foamy.

Combine wet ingredients: Add the egg, remaining sugar, vanilla extract, and melted butter to the yeast mixture. Whisk until well combined.

Add dry ingredients: In a separate bowl, whisk together the flour and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Don't overmix.

Prepare filling: In a small bowl, combine softened butter, brown sugar, and cinnamon. Mix until well blended.

Assemble muffins: Line a 12-cup muffin tin with paper liners. Divide the muffin batter evenly among the liners, filling each about halfway. Drop a spoonful (about 1-2 tablespoons) of the cinnamon filling into the center of each muffin. Swirl the filling slightly into the batter using a knife or toothpick. Do not overmix.

Proof muffins: Cover the muffin tin loosely with plastic wrap and let rise in a warm place for 30-45 minutes, or until almost doubled in size.

Bake: Preheat oven to 375°F (190°C). Bake for 18-22 minutes, or until golden brown and a toothpick inserted into the center comes out clean.

Cool: Let the muffins cool in the tin for a few minutes before transferring them to a wire rack to cool completely. Make frosting (optional): While the muffins are cooling, beat together the softened cream cheese and butter until smooth. Gradually add the powdered sugar, beating until light and fluffy. Stir in the vanilla extract and milk until desired consistency is reached. Frost the muffins once completely cool.