Preheat the oven to 400 F (200 C). Slice the top off the garlic head to expose the cloves, drizzle with olive oil, wrap in foil and roast for 30 to 35 minutes until soft and golden. Let cool slightly, then squeeze the roasted garlic into a small bowl and mash with a fork.
Place the potato chunks in a large pot and cover with cold water by about an inch. Add a generous pinch of salt. Bring to a boil over high heat, then reduce to a simmer and cook until potatoes are tender when pierced, about 15 to 20 minutes depending on size.
While potatoes cook, melt 2 tablespoons of butter in a small skillet over low heat. Add two to three cloves of finely minced raw garlic (or use a few spoonfuls of the roasted garlic for a milder, sweeter flavor) and gently sauté until fragrant and just golden, about 1 to 2 minutes. Remove from heat.
Drain the potatoes well and return them to the warm pot. Let them sit for a minute to steam off excess moisture. Use a potato masher, ricer, or hand mixer on low to break them up until mostly smooth.
Add the remaining butter, warmed milk or cream, sour cream if using, the mashed roasted garlic, and the sautéed garlic with butter. Stir gently until combined and creamy. If you prefer silkier texture, use a ricer or a hand mixer briefly, but avoid overworking which can make potatoes gluey.
Taste and season with salt and black pepper. Adjust butter or cream to reach your desired richness and texture.
Transfer the mashed potatoes to a serving bowl, top with a pat of butter, a drizzle of olive oil if you like, and sprinkle with chopped chives or parsley. Serve hot.