In a small saucepan set over medium heat, combine milk, water, and butter. Heat, stirring occasionally, until very warm (115-120 degrees F).
Pour the mixture into the bowl of a stand mixer. Sprinkle the yeast and sugar on top and allow to bloom for 10minutes.
Add 2 cups of flour, egg yolk, and salt. Using the paddle attachment, mix until a soft dough is formed, then switch to the hook attachment.
Mix on low speed for 8-10 minutes until the dough is slightly sticky to the touch, adding more flour a little at a time as needed.
Transfer the dough to an oiled bowl, turning it to coat all the sides. Cover and allow to rise in a warm place for 30-60 minutes, until doubled in size.
When dough has risen, transfer into a lightly floured work surface and knead out any air bubbles. Divide the dough into 12 equal pieces (about 1.50-1.80 ounces each), shaping them into balls. Place them 3x4 in a greased 8-inch square cake pan. Cover and allow to rest for 20-30 minutes, until doubled in size.
Meanwhile, preheat the oven to 375degrees F. Brush a bit of water over the raw rolls, then bake, uncovered, for 18-22 minutes, or until the tops are golden brown and baked through. Brush the rolls with melted butter and serve warm.