Preheat oven to 350 degrees. Place peeled sweet potato chunks and three cloves of garlic into a large oven safe pot. Add enough water to cover the potatoes. Bring to a boil over medium heat and continue to cook until potatoes can be easily pierced with a fork. The length of time will depend on the size of your cubed sweet potatoes. Mine took about 30 minutes. Drain potatoes and then add back to the oven safe pot. Using a potato masher, mash until they're light and fluffy. Stir in butter, milk, salt, thyme and pepper to taste. Stir in parmesan cheese and then put the pot into the oven for 5 minutes, allowing the parmesan cheese to fully melt. Remove from the oven, stir one last time, and then add the potatoes to a serving dish and top with diced green onions and additional parmesan cheese.