1Remove the seeds from the pumpkin and slice it into thin pieces. Blanch it in lightly salted water for about 4 mins, then drain and set aside.
2Wash the leek thoroughly and cut it into thin rings. Slice the champignons and king oyster mushrooms into thin pieces as well.
3In a large pan, heat some olive oil over medium heat. Add the minced garlic and sauté for about a minute. Add the butter, fresh sage, and thyme, and cook for 2-3 minutes. Deglaze the pan with a splash of sake or white wine.
4Add the leeks and cook for another 2-3 minutes.
5Pour in the cream and milk, letting the mixture simmer for 3 minutes. Season with salt, pepper, and a bit of grated nutmeg.
6Pour the leek and mushroom mixture into a baking dish. Layer the pumpkin slices on top.
7Grate fresh nutmeg and sprinkle the grated Gruyère and Pecorino cheese evenly over the top. Garnish with a few mushroom slices and sage leaves.
8Preheat the oven to 165°C. Bake the gratin for 25 minutes. If the cheese is browning too quickly, cover the dish with foil. Increase the temperature to 180°C and bake for an additional 15 minutes, or until the top is golden and bubbly.
9After baking, let the gratin rest for about 5 minutes. Serve drizzled with pumpkin seed oil and crispy fried sage leaves.