To make dough: Measure all dough ingredients into bread machine pan in the order suggested by manufacturer. Process on dough/manual cycle.
When cycle is complete, place dough in a greased bowl, turning to coat; cover tightly and refrigerate 2 to 24 hours.
Remove dough from refrigerator; punch down. Turn dough out onto floured surface. Divide dough into 12 equal pieces; divide each again into 3 pieces. Roll into smooth balls. Place three balls in each section of 12 greased muffin pan cups. Cover; let rise in warm, draft-free place until doubled in size, about 30 to 45 minutes.
Combine herb butter ingredients; brush on rolls. Bake at 375°F for 15 to 20 minutes or until done. Remove from pan; cool on wire rack.