Preheat your oven to 400°F. Slice off the top of the garlic head to expose the cloves, drizzle with olive oil, and wrap it tightly in foil. Roast for 40 to 45 minutes, until the cloves are soft and deeply golden.
While the garlic roasts, place your peeled and cubed potatoes into a large pot and cover with cold, salted water. Bring it to a boil, then reduce to a simmer and cook for 15 to 18 minutes, until a fork slides through easily.
Once the garlic head is cool enough to handle, squeeze the cloves out of their papery skins into a small bowl. Mash them lightly with a fork until you have a smooth, spreadable paste.
In a small saucepan, gently heat the butter and milk together just until the butter melts and everything is warm. Keeping it warm instead of cold helps the potatoes stay silky instead of turning gummy.
Drain the potatoes well and return them to the hot pot for a minute to let excess steam escape. Add the roasted garlic paste, warm butter and milk mixture, and sour cream if using, then mash everything together until creamy. Season with salt and pepper, and serve while hot.