Peel and cut potatoes into 2/3-inch cubes and place in a large bowl.
Add milk, cream, mayonnaise, thyme, garlic, salt, pepper, and shredded cheese (excluding mozzarella) to the bowl. Mix well to coat the potatoes evenly.
Pour the mixture into a 3-quart (3-liter) baking dish and cover tightly with foil.
Bake for 60 minutes or until the potatoes are tender when pierced with a fork.
Remove foil, sprinkle mozzarella cheese evenly on top, and return to the oven uncovered for 25 minutes, or until the top is golden and bubbly.
Let the bake rest for 5–10 minutes before serving. Garnish with extra thyme leaves if desired.