In a mixing bowl, whisk together sour cream, mayo, heavy cream, pressed (or grated) garlic, salt and pepper.
If you have a mandolin slicer, slice potatoes. (If you don't have one just slice them thin with a knife.) Slice mushrooms thin as well.
Spread some of the cream sauce on the bottom of the baking dish and start layering half of the potatoes. Don't stack the potatoes but rather overlap if you have to.
Spread half of mushrooms over potatoes, evenly. Spread half Mozzarella cheese and half of white cheddar cheese. Add some salt, pepper and thyme.
Repeat the second layer: remaining potatoes, remaining mushrooms, remaining cheese.
Pour cream sauce over the top, as evenly as possible.
Bake for 60-70 minutes until all potatoes are done. You can stick a knife slowly in the middle and feel how easily it goes through the potatoes.