In a saucepan, place the potatoes pieces, butternut squash, onion, garlic in a large wide saucepan and cover with water. Add some salt, and thyme. Bring to boil and simmer for 8-10 minutes until just softened.
Transfer the vegetables over onto a gratin dish. Check the seasoning. Pour over most of the liquid to ensure the vegetables are covered and sprinkle the cheese over.
Place in the oven for 35-40 minutes until cooked through and crispy.