In a medium bowl, combine the warmed milk and 1 tablespoon sugar. Sprinkle yeast over milk and whisk to blend. Let sit until yeast is foamy, about 5 minutes. Add eggs; whisk until smooth.
In the bowl of a stand mixer fitted with a dough hook, combine the remaining 4 tablespoons of sugar, flour, and salt. Add the milk mixture. With the mixer running on low, add butter, 1 piece at a time, blending well between additions.
Knead on medium speed for 1 minute. Knead on medium-high speed until the dough is soft, about 5 minutes.
Brush a medium bowl with some melted butter; place the dough in the bowl. Brush the top of the dough with the remaining melted butter; cover with plastic wrap.
Let dough rise in a warm, draft-free area until doubled in size, about 1 hour.
When ready, punch the dough, turn it out onto a floured surface, and roll it into a 10x15-inch rectangle (it should be about ¼-inch thick).