Preheat oven to 400°F. Drizzle olive oil over top of garlic and wrap in foil. Bake until golden and soft, about 45 minutes, then set aside.

Meanwhile, add potatoes to a large pot. Cover potatoes with a few inches of water (about 6 cups) and season with salt; cover pot and bring to a boil. After about 30 minutes, check if potatoes are soft (a knife should easily slide through them), then drain in a colander.

In a large bowl, mash or rice potatoes, then slowly add melted butter, cream, and roasted garlic. Add balsamic vinegar, season generously with salt, and garnish with parsley. Serve immediately.