Warm the milk slightly until it's just above room temperature (do not exceed 40°C/104°F). Stir in the yeast and 1 tablespoon of the sugar. Let it sit for 5-10 minutes until it becomes frothy.

In a large mixing bowl, combine the flour, remaining sugar, and salt. Add the melted butter, egg, and the frothy yeast mixture to the dry ingredients.

Mix until a soft dough forms. Knead the dough on a floured surface for 5-7 minutes until it becomes smooth and elastic.

Transfer the dough to a greased bowl, cover it with a towel, and allow it to rise in a warm place for 1 to 1.5 hours, or until it has doubled in size.

Once the dough has risen, roll it out on a floured surface into a large rectangle, about 1/4 inch thick.

Brush the entire surface of the dough with melted butter. Mix the brown sugar and cinnamon together, then evenly sprinkle the mixture over the buttered dough.

Carefully roll the dough into a tight log, starting from the long side. Slice the log into 12 equal pieces.

Arrange the rolls in a greased or parchment-lined baking dish, leaving a little space between each one. Cover the dish with a towel and let the rolls rise for another 30 minutes.

Preheat your oven to 350°F. Once the rolls have risen, bake them for 20-25 minutes, or until they are golden brown.

While the rolls are baking, mix the cream cheese and softened butter together until smooth.

Gradually add the powdered sugar and vanilla extract, mixing until fully combined. If the glaze is too thick, add milk a little at a time until you reach the desired consistency.

After baking, let the rolls cool slightly in the pan. Spread the cream cheese glaze over the warm rolls.