In a medium bowl, combine the milk and 1 tablespoon sugar. Sprinkle yeast over the milk and whisk to blend. Let sit until the yeast is foamy, about 5 minutes.
Add eggs. Whisk until smooth.
In the bowl of a stand mixer with a dough hook attachment, combine the remaining 4 tablespoons sugar, the flour, and the salt.
Add the milk mixture. With the mixer running, add butter, 1 piece at a time, blending well between additions.
Knead on medium speed for 1 minute. Increase the speed to medium-high speed and knead until the dough is soft (about 5 minutes). Add more flour, a tablespoon at a time, if the dough doesn't come together. Or, add more water if too dry.
Brush a medium bowl with the melted butter. Place the dough in the bowl and flip to coat with the butter. Cover with plastic wrap.
Let the dough rise in a warm, draft-free area until doubled in size (about 1 hour).
When you are ready, punch the dough, turn it out onto a floured surface, and roll it into a 10x15-inch rectangle. (It should be about 1/4-inch thick.)