Preheat oven to 375 F.
Wrap the garlic in foil, leaving a small opening to pour olive oil through. Drizzle on the olive oil, then close up the foil. Bake until soft, about 45-60 minutes. Let cool before handling.
Add potatoes, 1 tbs salt, and enough water to cover the potatoes to a large pot. Bring to a boil over high heat and reduce to a simmer and cook until tender, about 20 minutes.
Drain the potatoes and return to the pot. Turn pot on low heat and let potatoes rest until they stop steaming, about 5 minutes.
Turn off the heat and add the garlic to the potatoes. Mash together to combine and get ride of excessive lumps.
While the potatoes are still hot, add the melted butter, goat cheese, and heavy cream. Mix until smooth.
Add salt and pepper to taste, garnish with fresh parsley, and enjoy.