In a medium saucepan over medium heat, whisk together heavy cream, garlic, thyme, rosemary, basil and nutmeg until heated through, about 1-2 minutes.
Next, add a layer of the sliced potatoes to a 4-qt slow cooker in an overlapping pattern and season with salt and pepper.
Pour 1/3 cup of the cream mixture over the potatoes and sprinkle some shredded Gruyere and cheddar cheese on top. Repeat with remaining potato slices, cream mixture, and Gruyere and cheddar cheese to create 2 more layers.
Cover and cook on high heat for 4-5 hours, or until the potatoes are tender.
Sprinkle parmesan cheese on top. Cover and cook again until melted, about 5-10 minutes.
Uncover and let potatoes rest for 15 minutes, before serving.