Mix 1 cup warm milk, 1 tablespoon sugar, and active dry yeast together and let sit for 10 minutes until a thin layer of foam forms
In a mixing bowl, combine 3 ½ cups flour, 2 tablespoons sugar, 1 egg, ¼ cup melted butter, 1 teaspoon salt, and the yeast mixture
Mix with dough hook for about 10 minutes, then knead by hand for a couple minutes until smooth
Oil a bowl, add dough, cover and let rise for 1 hour until doubled in size
Punch down dough and roll into a rectangle or oval shape
Mix filling of ⅓ cup softened butter, ⅔ cup brown sugar, and 2 tablespoons cinnamon until combined
Spread filling evenly over dough and roll up tightly from the back
Cut into 8 pieces and place in a greased baking dish
Cover and let rest for 30 minutes until puffy
Bake at 350°F until golden brown
While baking, whisk together 1 cup powdered sugar and 3 tablespoons milk for icing
Brush icing over warm cinnamon rolls immediately after removing from oven
