Preheat the oven to 400 degrees.
In a small baking dish, drizzle olive oil over the head of garlic. Roast for 30-35 minutes until the garlic is golden and tender.
Carefully remove from the oven and set aside to cool.
Meanwhile, in a large pot, place the potatoes and cover with cold water. Boil until the potatoes can easily be pierced with a fork.
Drain the potatoes, and return to the pot.
Add in the hot milk, and roughly mash the potatoes with a fork. With a mixer on low or medium low, begin to whip the potatoes.
Add in the butter chunk by chunk, adding in a splash more milk or two if needed to loosen.
Add the goat cheese in chunks.
Add the cloves of garlic. Season to taste with salt and pepper.
Use 3/4 of the chives to mix in to the potatoes, and sprinkle the rest on top.