Melt the butter in the microwave for 1 minute, then let it cool slightly. Warm the milk to about 35 °C, then add the yeast and let it sit for 5 minutes.
In the mixer bowl, add the salt, flour, and sugar in that order. Add the milk-yeast mixture, the melted and cooled butter, and the beaten egg. Knead with the dough hook on low speed for about 20 minutes.
Transfer the dough to a mixing bowl, cover with a clean dish towel, and let it rise in a warm place for 1 hour, until it doubles in size. The dough may be slightly sticky at this stage.
For the filling, cream the butter with a spatula, then add the cinnamon, sugar, and salt. Mix until the mixture is smooth, creamy, and easy to spread.
Flour the work surface, punch down the dough, then roll it out into a rectangle measuring about 45 × 30 cm. Spread the filling evenly over the dough, then roll it up tightly to form a 45-cm log.
Cut the cinnamon rolls into pieces every 3 cm. Place the rolls side by side in a large, buttered baking dish or individually on a baking sheet lined with parchment paper, spacing them apart. Cover and let rise again for 1 hour.
For a nice golden color, brush the cinnamon rolls with a little milk, if desired. Preheat the oven to 180 °C, then bake for 18 to 20 minutes.
For the glaze, mix the cream cheese, milk, powdered sugar, and natural vanilla extract until the mixture is smooth and well combined. Spread the glaze over the cinnamon rolls while they’re still warm before serving.
