Add 1 Tbsp sea salt to the boiling water, then add the daikon slices. Cook until tender but still holding their shape, about 10 minutes. Drain and rinse with cold water, then pat dry with paper towels.

Preheat your oven to 350°F (175°C) and position the rack in the upper third. Grease an 8 x 10-inch casserole dish with 1 Tbsp melted butter and coat one side of a large piece of aluminum foil with the remaining butter.

In a small saucepan over medium-high heat, combine the heavy cream, remaining sea salt, pepper, dried thyme, onion powder, and garlic powder. Bring to a simmer and reduce the heat to low, letting it simmer until reduced by about one-third, approximately 6 to 8 minutes. Stir in the remaining butter and set aside.

In the prepared casserole dish, layer one-third of the daikon slices, overlapping slightly. Sprinkle one-third of the shredded cheddar and Gruyere cheeses on top. Repeat the layering two more times, finishing with the remaining cheese. Pour the reduced cream mixture over the layers.

Cover the dish with the prepared aluminum foil and bake for about 45 minutes until the cheese is light golden brown and the liquid is bubbling. Remove the foil, sprinkle Parmesan cheese on top, and bake uncovered for an additional 15 minutes. Switch the oven to broil and broil the gratin for 1 to 2 minutes until the crust is deep golden brown and bubbling. Let stand for 10 minutes before serving.