In a medium saucepan, heat milk with 3 Tbsp. of butter and sugar, until the butter melts. Transfer to large bowl, cool slightly. Stir in yeast, let stand until dissolved, about 5 min. Add 4 cups of flour and salt, stir until soft sticky dough forms.
Turn the dough out onto a lightly floured surface and knead until silky, about 4 minutes. Transfer the dough to a lightly oiled bowl, cover with plastic wrap, let rise in a warm spot until doubled in bulk, about 1 hr.
In a small shallow bowl, mix cheese with parsley, thyme and rosemary. Melt the remaining 8 Tbsp. of butter.
Lightly butter 18 of the cups in 2 or more non stick muffin pans. Punch down the dough and divide it into 3 equal pieces. Working with 1 piece at a time and keeping the rest covered, roll into a 1-inch-thick rope, cut the rope into 18 equal pieces; roll each piece into a ball. Dip half of each ball into the melted butter and then into the herb-cheese mixture and arrange 3 balls in each prepared muffin cup, coated sides touching in the center. Repeat with the remaining dough and topping. Brush the top of the rolls with the remaining melted butter. Cover the muffin pans with plastic wrap and refrigerate overnight.
Loosely re-drape the plastic wrap over the muffin tins. Let the rolls rise in a warm spot until they are about 1” above the rim of the cups, about 2 hrs.
Preheat the oven to 425°. Bake the rolls in the lower and middle thirds of the oven for about 15 min., or until golden and sizzling; shift the pans halfway through from top to bottom and back to front for even browning. Turn the rolls out onto a rack and let cool slightly before serving.
Make Ahead: The rolls can be baked earlier in the day. Reheat before serving.