Pour the warm water into a large glass measuring cup, sprinkle in the yeast and 1/4 teaspoon sugar, stir until dissolved, and let it sit while preparing the milk mixture until it is a little foamy and smells yeasty.

In a separate bowl, warm the whole milk and 1/4 cup butter until the mixture reaches about 100 to 110°F and the butter is melted, then slowly dribble in the lightly beaten egg while mixing constantly so it does not scramble.

In a large bowl, whisk together 5 cups of the flour, the salt, and the remaining 1/2 cup sugar, then make a hollow in the center and pour in both the yeast mixture and the milk mixture.

Use a big spoon or sturdy spatula to pull the flour from the sides into the wet center, mixing and adding flour as necessary until the dough forms a soft ball that can be turned onto a floured counter without clinging excessively.

Knead the dough for 10 minutes, adding flour as needed to keep it from sticking to your hands and the counter.

Spray a large bowl or proofing container with cooking spray, place the dough inside, spray the top of the dough, cover with a lid or plastic wrap, and let it rise for 2 hours or until doubled in size.

Gently punch down the dough and divide it into two equal portions, returning one half to the bowl and covering it while shaping the first batch; divide the uncovered half into 12 pieces.

Roll each piece into a rope about 5 inches long, tie it into a simple knot, tuck the ends slightly if needed, and place the rolls on a cookie sheet sprayed with cooking spray or lined with a silicone mat.

Spray the tops lightly with cooking spray, cover with a clean towel, and let the rolls rise for 30 to 45 minutes, then repeat the shaping and rising with the remaining half of the dough using two baking sheets so the rolls do not bake into each other.

Preheat the oven to 365°F and bake the rolls for 20 minutes, until they are golden on top and lightly browned underneath.

Remove the rolls from the oven, brush the tops with butter while they are warm, and let them cool on a rack or serve warm.