Preheat the oven to 400 degrees F. Melt 2 tablespoons butter in a large ovenproof skillet over medium-high heat. Add the onion and thyme and cook, stirring, until the onion softens, about 5 minutes.
Meanwhile, combine the butternut and kabocha squash in a large microwave-safe bowl with 1 cup water. Cover with plastic wrap and microwave until the squash is just tender, about 5 minutes. Drain and add the squash to the skillet along with the garlic, mace, 1 teaspoon salt and a few grinds of pepper. Cook, stirring, about 3 minutes. Add the broth and cook until it is mostly absorbed, about 5 more minutes. Stir in the heavy cream and cook until slightly thickened, 2 minutes.
Melt the remaining 1 tablespoon butter in the microwave and toss with the breadcrumbs, parmesan and parsley; season with salt and pepper. Sprinkle over the squash, then top with the gruyere. Transfer the skillet to the oven and bake until golden, about 30 minutes. Let rest 5 minutes before serving.
How to break down butternut squash:
Cut about 1 inch off the bottom end with a chef's knife. Scoop out the seeds.
Hold the squash against your body and remove the skin with a vegetable peeler; chop.
How to break down kabocha squash:
Quarter the squash with a chef's knife, then scoop out the seeds.
Put each quarter flat-side down and cut off the skin with a paring knife; chop the squash.