In a small bowl, stir together the warm water, yeast, and 1 Tablespoon sugar. Cover with a paper towel. Let sit 5 minutes, or until bubbly.
In a stand mixer fitted with a dough attachment, stir together melted butter, milk, salt, and the remaining 4 Tablespoons sugar. Stir in yeast mixture until combined. Add 1 cup flour and stir until smooth. Add the remaining flour 1/2 cup at a time. Knead 1 to 2 minutes. If the dough is too sticky, add a little more flour until smooth and soft..
Cover the bowl with plastic wrap and place in a warm spot. Let rise about 20 minutes.
Preheat the oven to 350°F. Butter a pie dish.
Once your dough has risen, punch it down and roll out on a floured surface. You want to form a rectangle, approximately 10×12 inches. It doesn’t have to be perfect. Spread softened butter onto the dough with a brush and then sprinkle the filling evenly over the top. Gently press the sugar down into the butter. Roll the doll, length-side, into a swirl.
Cut the dough into 1-inch pieces with floss or a large knife. Place rolls, swirl-side up, into pie dish, about 1 inch apart. Let rolls rise about 15 minutes.
Bake 18 to 20 minutes, or until golden brown. Remove from oven and let cool.