Preheat the oven to 400°F (200°C). Slice the top off the garlic head to expose the cloves, place it on a piece of foil, drizzle with olive oil, season lightly with salt, wrap tightly, and roast for 35–40 minutes until soft and caramelized. Once cool enough to handle, squeeze the roasted garlic cloves from their skins into a small bowl and mash into a paste.
While the garlic roasts, peel (if desired) and cut potatoes into even 1–2 inch chunks so they cook at the same rate. Place them in a large pot and cover with cold water by about an inch. Add 1/2 teaspoon salt to the water and bring to a boil over high heat.
Reduce to a simmer and cook the potatoes until fork-tender, about 12–18 minutes depending on size. Test by piercing a chunk with a fork; it should slide off easily without being mushy.
Drain the potatoes thoroughly in a colander and return them to the warm pot over the turned-off burner for a minute to let excess steam escape—this helps keep the mash from getting watery.
Warm the milk and butter together in a small saucepan or in the microwave until the butter melts and the liquid is hot but not boiling. This helps the potatoes absorb it more easily and stay warm.
Mash the potatoes using a potato masher or ricer for the smoothest texture. Add the roasted garlic paste, warm butter-and-milk mixture, the remaining salt (to taste), and black pepper. Fold in sour cream or crème fraîche if using. Mash or stir until you reach your preferred consistency—smooth and silky or slightly chunky.
Taste and adjust seasoning—more salt, a splash of milk for looseness, or a knob of butter for richness. Stir in chopped chives for a fresh finish, and drizzle a little olive oil over the top if desired.
Transfer to a warm serving bowl, add an extra pat of butter on top to melt, and serve immediately while piping hot.