Pour warmed milk into a large mixing bowl and sprinkle yeast over the top. Let sit for 1 minute, then stir gently to activate the yeast.

Add granulated sugar, melted butter, egg, and salt to the yeast mixture and stir until combined.

Gradually add flour, one cup at a time, mixing on low speed for 8 to 10 minutes until dough is smooth and slightly sticky.

Transfer dough to a lightly oiled bowl, cover with a damp towel, and let rise in a warm spot for 1 hour or until doubled in size.

While dough rises, mix softened butter, brown sugar, and cinnamon in a small bowl until well combined.

Turn risen dough onto a floured surface and roll into a 12x9-inch rectangle, about 1/2 inch thick.

Spread cinnamon-sugar filling evenly over dough, leaving a 1/2-inch border. Roll tightly from the long side and pinch seam to seal.

Cut the log into 12 equal 1-inch slices and place cut-side up in a buttered 9x13-inch pan, spacing them evenly.

Cover rolls with plastic wrap and let rise for 30 to 45 minutes until puffy and nearly touching.

Preheat oven to 375°F and bake rolls for 18 to 22 minutes until light golden brown.

While rolls bake, melt butter in a small saucepan, then whisk in powdered sugar, vanilla, salt, and milk until glaze is smooth and pourable.

Remove rolls from oven and let cool for 3 to 5 minutes, then pour glaze over warm rolls and serve.