Dissolve the yeast in the water with 1 teaspoon sugar. Let sit until foamy.
Combine the yeast mixture, milk, sugar, eggs and 1 cup flour. Beat with an electric mixer until well combined.
Add the flour to the mixture. When the dough comes together, turn it out on a floured surface, and knead for about 5 minutes, until elastic. Knead in the salt, then place the dough in an oiled bowl. Cover with a dishtowel. Allow to rise in a warm place for about 1 hour, or until it has doubled in size.
Punch down the dough, then divide into 30 small portions. Roll each of the portions into a ball, and then evenly space the balls on a greased baking sheet. Cover once more with a dishtowel, and allow to rise about 1 hour, or until doubled in size.
Preheat the oven to 350 F.
Bake the rolls for 15 to 20 minutes. As soon as they come out of the oven, brush them with butter. Serve with more softened butter, if desired.