Combine warm milk, 3 tablespoons melted butter, 1 tablespoon sugar, and yeast in the bowl of a stand mixer. Let stand until lightly bubbling, about 6-8 minutes.
Add lightly beaten egg, remaining sugar, and 1 cup flour to bowl. Stir using a rubber spatula or wooden spoon until lightly combine. Allow to sit for 10 minutes.
Add 2 1/2 cups of flour and 1/2 teaspoon salt to liquid mixture, and using the dough hook attachment on your stand mixer, mix the dough until a soft dough ball forms.
Add dough to a lightly floured surface and knead for about 10 minutes until dough is soft and pliable. Spray a large bowl and add dough. Cover with a kitchen towel and place in a warm spot in your kitchen. Allow to rise until doubled in size. This should take between 45 minutes to an hour, depending how warm your home is. Punch dough down, and allow to rise a second time. Punch dough down again, and allow to rest for 5 minutes.
On a floured surface, roll dough out to about 16 by 10 inches. Place the long edge closest to you.
Spread 8 tablespoons (1 stick) of room temperature butter over the dough. Combine brown sugar, cinnamon, and 1/2 teaspoon salt in a small bowl. Sprinkle over the buttered dough.
Starting from the edge closest to you, begin rolling the dough like a jelly roll until you have one long log.
Use a knife to score the dough into 12-15 uniform slices. Place cut side up in a greased 9 x 13 baking dish. Cover with a towel, and allow to rise in a warm place until doubled in size, about 20-30 minutes.
Preheat oven to 350 degrees. Bake rolls for 25 minutes until lightly golden brown.