Roast the garlic first since this step takes the longest. Preheat your oven to 400 degrees Fahrenheit. Slice the top quarter off the head of garlic to expose the cloves, drizzle with olive oil, and wrap it tightly in foil. Place it on a small baking sheet and roast for 40 to 45 minutes until the cloves feel completely soft when you press on them and they are golden at the tips. Let it cool until you can handle it, then squeeze the softened cloves out into a small bowl and mash them into a smooth paste with a fork. Set aside. If making a day ahead, refrigerate in a covered container.

Place the peeled, chunked potatoes in a large pot and cover with cold water by about 2 inches. Add a generous pinch of salt, enough to make the water taste lightly seasoned. Bring to a boil over high heat, then reduce to a steady simmer and cook for 15 to 18 minutes. The potatoes are ready when a fork slides in with no resistance at all. Do not under-cook them; dense potatoes never mash smoothly.

Drain the potatoes thoroughly in a colander and return them to the warm pot. Set the pot over low heat for about 1 minute, shaking it gently. This dries out any lingering moisture, which is one of the small steps that keeps mashed potatoes fluffy instead of watery.

Add the softened cream cheese, softened butter pieces, and roasted garlic paste to the hot potatoes. Mash everything together with a potato masher or a hand mixer on low speed until smooth. Add the warmed milk or cream in two additions, stirring after each, until the potatoes reach the consistency you like. They should be creamy and just loose enough to fall slowly from a spoon. Season with salt and pepper, taste, and adjust.

Transfer to a serving bowl, make a shallow well in the center, and add an extra pat of butter if you like. Garnish with sliced chives. Serve immediately, or keep warm covered in a low 200-degree oven for up to 30 minutes with a piece of foil pressed directly on the surface to prevent a skin from forming.