Warm 1 cup milk
Add 2 1/4 teaspoons active dry yeast and 1/4 cup sugar
Let sit for 5 to 10 minutes
Mix in 1/4 cup melted butter, 1 egg, and 1/2 teaspoon salt
Add 3 to 3 1/2 cups all-purpose flour
Knead until smooth and elastic
Place dough in a greased bowl
Cover and let rise until doubled
Roll dough into a rectangle
Spread softened butter over the dough
Sprinkle with brown sugar and cinnamon
Roll up tightly into a log
Cut into even pieces
Place pieces in a greased baking dish
Cover and let rise again
Bake at 350°F until golden brown
Mix powdered sugar, milk, and vanilla for icing
Drizzle icing over warm buns