In a small bowl, combine warm milk, yeast, and 1 tablespoon of sugar. Let it sit for 5-10 minutes until foamy.
In a large bowl, whisk together flour, remaining sugar, and salt. Make a well in the center.
Pour the yeast mixture, melted butter, and egg into the well. Mix until a shaggy dough forms. Turn out onto a floured surface and knead for 8-10 minutes until smooth and elastic.
Place the dough in a greased bowl, cover, and let rise in a warm place for 1-1.5 hours, or until doubled in size.
While the dough rises, prepare the filling. In a small bowl, mix brown sugar and cinnamon. In another bowl, cream together softened butter.
Once the dough has risen, punch it down and roll it out into a large rectangle on a floured surface.
Spread the softened butter evenly over the dough, leaving a small border. Sprinkle the cinnamon-sugar mixture over the butter.
Roll up the dough tightly from the long edge. Cut the roll into 12 equal slices.
Place the rolls in a greased baking dish. Cover and let rise for another 30-45 minutes.
Preheat oven to 375°F (190°C). Bake for 18-20 minutes, or until golden brown.
While the rolls are baking, prepare the glaze. In a bowl, beat together softened cream cheese and butter until smooth. Gradually beat in powdered sugar, milk, and vanilla extract until smooth and creamy.
Let the rolls cool slightly in the pan before drizzling with the cream cheese glaze.