Preheat oven to 400F. Cut the top off the garlic head, drizzle with olive oil, wrap in foil, and roast for 40 minutes.
Peel and cut potatoes into even chunks. Boil in a large pot of salted water for 15 to 20 minutes until fork-tender.
Drain the potatoes well and return them to the hot pot for 1 minute to evaporate any excess moisture.
Mash the potatoes until completely smooth. Squeeze the roasted garlic cloves out of their skins directly into the pot.
Stir in the melted butter, warm heavy cream, salt, black pepper, parsley, rosemary, and parmesan cheese until creamy and fully combined. Serve immediately.