In a medium saucepan, whisk together heavy cream, garlic, dried thyme, and nutmeg over medium heat until heated through, about 1-2 minutes.
Add a layer of potatoes to a 4-qt slow cooker in an overlapping pattern; season with salt and pepper, to taste. Pour one-third of the cream mixture over potatoes; sprinkle with Gruyere. Repeat with remaining potato slices, cream mixture and Gruyere to create 2 more layers.
Cover and cook on high heat for 4-5 hours, or until potatoes are tender. Sprinkle with Parmesan. Cover and cook until melted, about 5 minutes.
Remove lid and let potatoes rest for 15 minutes, allowing the sauce to thicken as it sits.