Slice zucchini on an angle into ¼ inch pieces. Salt generously and drain on layered paper towels for 30 minutes.
Divide butternut squash between two baking sheets along with the smashed garlic. Drizzle 2 tablespoons of olive oil over each pan, season with salt and pepper, and toss to coat. Spread the squash and garlic into even layers and bake until lightly golden and tender, 25 – 30 minutes. Let cool.
Pat zucchini dry, place on baking sheets, and cook until tender, about 10 – 15 minutes. Let cool. Lower the oven temperature to 375ºF.
Combine the ricotta cheese with eggs, mozzarella cheese, half the parmesan cheese, 1 teaspoon each salt and pepper, and the nutmeg.
Melt butter in a small pan over medium-high heat. As soon as it starts to sizzle, add the sage and cook until it starts to brown, about 2 minutes.
Put cooled butternut squash and garlic in a large mixing bowl and mash with a potato masher. Stir in the melted butter and sage.
Spray a deep 10×14-inch baking pan with cooking spray. Spread a thin layer of ricotta cheese mixture on the bottom. Top with 1 layer of zucchini and spread half the butternut squash mixture over the top. Add another layer of zucchini and top with half the remaining ricotta cheese mixture. Add another layer of zucchini, the rest of the ricotta, the rest of the zucchini, and the rest of the butternut squash mixture. Sprinkle the remaining parmesan cheese over the top and bake for 35 – 45 minutes or until golden and hot. Let sit 15 minutes before cutting.