Warm 1 cup milk to about 110°F
Mix warm milk, 2 1/4 teaspoons active dry yeast, and 1 tablespoon sugar
Let sit 5 to 10 minutes until foamy
Add 1/4 cup melted butter, 1/4 cup sugar, 1 egg, and 1/2 teaspoon salt
Mix in 3 to 3 1/2 cups all-purpose flour until a soft dough forms
Knead the dough for 5 to 8 minutes until smooth
Place dough in a greased bowl and cover
Let rise for 1 to 1 1/2 hours until doubled
Roll dough into a rectangle
Spread softened butter over the dough
Sprinkle with brown sugar and cinnamon
Roll the dough tightly into a log
Cut into even slices
Place slices 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 powdered sugar, milk, and vanilla for icing
Spread icing over warm rolls