Preheat the oven to 400°F. Generously grease a 9×13-inch baking dish.
Scrub the potatoes and cut each in half crosswise. Working with one half at a time, attach the flat, cut side to the prongs of an apple peeler/corer/spiral slicer. Run through the machine to peel, remove the center and spiral-slice. Small remnants of peel are fine.
3 medium russet potatoes
Gently keep each potato spiral assembled and arrange the six halves cut-side down in the prepared dish, with their hollow centers accessible from above.
Stir together the melted butter, garlic and thyme. Divide evenly among the six potato cavities.
2 Tbsp salted butter, 2 cloves garlic , 1/2 tsp dried thyme
Loosely fill the remaining space in each cavity with Gruyère, reserving any leftover cheese for the topping.
1 cup freshly shredded Gruyère cheese
Slowly drizzle the heavy cream over each potato, allowing it to run into the layers and pool in the dish. Sprinkle the potatoes and cream with salt, pepper and Parmesan.
1 cup heavy whipping cream, 1/2 tsp fine salt, 1/4 tsp black pepper, 2 Tbsp grated Parmesan cheese
Cover the dish tightly with foil and bake for 45 minutes.
Carefully remove the foil and check the potatoes with a thin knife. It should slide easily through the layers without firm resistance. If needed, re-cover and bake until tender before proceeding.
Leave the foil off and sprinkle the reserved Gruyère over the potatoes. Bake uncovered for another 10 minutes, until the cheese is melted and the sauce is bubbling.
Let stand briefly before serving. Spoon the cream sauce from the pan over each potato half.