Warm 1 cup milk to about 110°F
Stir in 2 1/4 teaspoons active dry yeast and 1 tablespoon sugar
Let sit 5 to 10 minutes until foamy
In a large bowl, mix 1/4 cup sugar, 1/4 cup melted butter, 1 egg, and 1/2 teaspoon salt
Add the yeast mixture
Gradually mix in 3 to 3 1/2 cups all-purpose flour
Knead the dough for 5 to 8 minutes until smooth and elastic
Place dough in a greased bowl
Cover and let rise for 1 to 1 1/2 hours until doubled
Roll dough into a rectangle on a floured surface
Spread 1/4 cup softened butter over the dough
Mix 1/2 cup brown sugar and 1 to 2 tablespoons cinnamon
Sprinkle the cinnamon-sugar mixture evenly over the butter
Roll the dough tightly into a log
Cut into 12 equal rolls
Place rolls in a greased baking dish
Cover and let rise for 30 to 45 minutes
Bake at 350°F for 20 to 25 minutes until golden brown
Mix 1 cup powdered sugar, 2 tablespoons milk, and 1/2 teaspoon vanilla for the glaze
Drizzle glaze over warm rolls