Preheat oven to 400°F (205°C). Grease a baking dish with butter.
Slice sweet potatoes, golden potatoes, and purple potatoes thinly with a mandoline.
Mix cream, Gruyère, garlic, thyme, and salt in a bowl.
Add sliced vegetables to the creamy mixture; toss to coat thoroughly.
Layer soaked vegetables in the dish; pour any remaining mixture on top.
Cover with parchment paper, then foil; bake for 40 minutes until tender.
Remove foil and parchment; bake uncovered for 10-15 minutes until golden.
Sprinkle with Parmesan before serving; cool slightly and enjoy!
