In a small saucepan, bring the milk to a scalding temperature, stirring frequently. Remove immediately from heat after scalding.
Meanwhile, combine 1/3 cup butter, sugar, and salt in a medium bowl. Pour scalded milk over the top and cool to 110°F to 115°F, stirring occasionally. Whisk in the eggs.
While the scalded milk mixture is cooling, soften (bloom) the yeast in the warm water for 5 minutes.
In an electric mixer fitted with the dough hook attachment, combine 4 ½ 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°F to 85°F) 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°F to 85°F) until doubled in size, about 30 to 45 minutes.
Meanwhile, preheat the oven to 325°F. 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 warm.