In a small bowl, combine the yeast, sugar, and warm milk. Let it sit for 5-10 minutes until frothy.
In a large mixing bowl, combine the flour and salt. Add the egg, melted butter, and the yeast mixture. Mix until a dough forms.
Knead the dough on a lightly floured surface for about 8-10 minutes until smooth and elastic. Place in a greased bowl, cover, and let rise for 1 hour or until doubled in size.
Once the dough has risen, roll it out into a rectangle approximately 12x8 inches.
Spread the softened butter evenly over the dough. Mix the brown sugar and cinnamon together in a small bowl, then sprinkle it over the buttered dough.
Starting from the long edge, roll the dough tightly into a log and pinch the seam to seal. Slice the log into 8-10 equal pieces.
Place the rolls into a greased baking dish, leaving a little space between each roll. Cover and let them rise for another 30 minutes.
Preheat the oven to 375°F. Bake the rolls for 20-25 minutes or until golden brown.
While the rolls are baking, prepare the glaze by whisking together powdered sugar, milk, and vanilla extract until smooth.
Once the rolls are out of the oven, drizzle the glaze over them while still warm. Serve immediately and enjoy!
Notes
You can substitute almond milk for regular milk if desired. For a richer flavor, add a pinch of nutmeg to the filling.