Preheat your oven to 375°F and lightly oil a 9x13-inch baking dish. Cut butternut squash into 1-inch cubes, removing seeds and skin. Cook cubed squash in boiling salted water for 8-10 minutes until fork-tender, then drain thoroughly in a colander.
While squash cooks, melt butter with olive oil in a large skillet over medium heat. Add diced onion and sauté for 4 minutes until softened, then add minced garlic and cook 1 minute more until fragrant.
Pour vegetable broth into the skillet and bring to a simmer. Let it reduce by half, approximately 5-7 minutes, concentrating the savory flavors throughout.
Transfer cooked squash to a large mixing bowl and mash gently, leaving some small chunks for texture. Stir in the broth mixture, heavy cream, parmesan, eggs, sage, and thyme until well combined. Season with salt and pepper to taste.
Prepare this cozy fall squash casserole crowd recipe by pouring the mixture into your prepared baking dish. Combine breadcrumbs with 1 tablespoon melted butter and sprinkle evenly across the top, then scatter gruyere cheese over the breadcrumbs.
Bake for 25-30 minutes until the top turns golden brown and the edges bubble gently. A knife inserted in the center should reveal a set but slightly creamy interior. Let rest 5 minutes before serving.