Using scissors, cut each roll into sixths. (Cut each roll in half. Cut each half into 3 pieces.) Place in a bowl and pour butter on top.
Add the ranch packet and shredded cheese to the bowl. Gently toss until the dough is coated. Some pieces may stick together, and that's okay.
Place stacks of monkey bread on a prepared baking sheet (lightly greased or lined with parchment or a silicone baking mat) a few inches apart. About 8 stacks. The closer the bread pieces are to each other the softer the bread will be. Alternately spread them apart across the whole baking sheet for crispier bites. Cover with greased plastic wrap and let rise for 30-45 minutes, until puffy looking.
Bake at 350 degrees Fahrenheit for 15-20 minutes, until golden brown. Serve warm, with olive oil and balsamic vinegar, if desired. Enjoy!