Activate the yeast: In a small bowl, combine the warm milk, melted butter, and granulated sugar. Sprinkle the yeast over the mixture and let it sit for 5-10 minutes until foamy.
- Mix the dough: In a large bowl, combine flour and salt. Add the activated yeast mixture and egg. Stir with a wooden spoon until a dough forms. Knead the dough for 5-7 minutes on a floured surface until smooth and elastic.
- Let the dough rise: Place dough in a greased bowl, cover with a kitchen towel, and let rise for 1-1.5 hours, or until doubled in size.
- Prepare the filling: Mix softened butter, brown sugar, cinnamon, and a pinch of salt in a bowl until smooth and combined.
- Assemble the cinnamon rolls: Punch down the dough and roll it into a 12×18-inch rectangle on a floured surface. Spread the cinnamon filling evenly, leaving 1 inch along the edges. Roll the dough tightly, pinch the seam, and cut into 12 pieces.
- Arrange the rolls: Grease a 10-inch cast-iron skillet and arrange rolls inside. Cover with a towel and let rise for 30-40 minutes until puffed up.
- Preheat the oven to 350°F (175°C). Bake the rolls for 20-25 minutes, until golden brown and bubbly.
- Prepare the glaze: Mix softened cream cheese, powdered sugar, milk, vanilla extract, and a pinch of salt in a bowl. Whisk until smooth and creamy.
- Glaze and serve: After the rolls are baked, drizzle the cream cheese glaze over the warm rolls. Serve immediately.