In a small saucepan, bring the milk to a scalding temperature (170 degrees). Remove immediately from heat.
Meanwhile, combine 1/3 cup butter, sugar, and salt in a medium bowl. Pour scalded milk over the top and cool to 110 degrees to 115 degrees, stirring occasionally. Whisk in the eggs.
While the scalded milk mixture is cooling, soften (bloom) the yeast in the warm water (110 degrees) for 5 minutes.
In an electric mixer fitted with the dough hook attachment, combine 4 1/2 cups flour, yeast, and water. With the motor running on low, slowly drizzle in the scalded milk mixture.
Increase the mixer speed to medium and mix until shiny and smooth, 6 to 10 minutes. If the dough is sticky after 3 minutes, add the remaining ½ cup flour, 1 tablespoon at a time, until the dough comes together. Using a small, microwave-safe dish, melt the remaining butter for 15 to 20 seconds.
Turn out the dough onto a heavily floured surface and shape into a ball. Place in a greased bowl and brush with 1 teaspoon melted butter. Cover the bowl with plastic wrap and let rise in a warm place (80 degrees to 85 degrees, see recipe notes) until doubled in volume, about 2 hours.
Coat 3 or 4 baking sheets with nonstick cooking spray. Turn out the dough onto a lightly floured surface and divide into 4 equal portions of dough. Working with 1 portion of dough at a time, roll the dough into a 10-inch circle. Using a knife or a pizza cutter, cut each circle into 8 wedges.
Starting at the wide end of a wedge, roll up the dough. Place each roll 2 inches apart on the prepared baking sheets with the pointed tip on the bottom. Repeat with remaining wedges and portions of dough.
Cover the rolls with plastic wrap and let rise in a warm place (80 degrees to 85 degrees) until doubled in size, about 30 to 45 minutes.
Meanwhile, preheat the oven to 325 degrees. Bake, 2 sheets at a time, until the rolls are golden brown, about 20 to 25 minutes. Switch the positions and rotate the orientation of the sheets halfway through baking time. Remove from the oven and immediately brush with the remaining melted butter. Serve hot or at room temperature.
To create a warm environment ideal for rising:
Preheat your oven to its minimum temperature (170 degrees, 200 degrees, etc.), but shut it off once the temperature reaches 110 degrees.
Place your dough (in a greased bowl, covered with plastic wrap), on a baking sheet and in the oven. The oven temperature will drop when you open the oven door, but enough residual heat will remain that your dough should steadily rise.
In this recipe, the dough should double in 90 minutes to 2 hours under these conditions.