Preheat the oven to 375°F.

Oil a large rimmed baking sheet and arrange the sweet potatoes on top in an even layer, overlapping the slices as needed. Roast until tender, 15 to 20 minutes.

Meanwhile, in a very large skillet over medium-high heat, cook the sausage, stirring and breaking it up, until lightly browned and almost cooked through, 4 to 5 minutes. Add the onions and cook, stirring occasionally, until the sausage is cooked through and the onions are tender, 5 to 6 minutes. Add the garlic, 1 1/2 teaspoons of the salt, and 1 1/2 teaspoons of the pepper and cook until fragrant, 30 to 60 seconds. Stir in the marinara and cook, stirring occasionally, until the sauce thickens slightly, 4 to 5 minutes. Remove from the heat, add more salt and pepper to taste, and set aside.

While the marinara mixture is simmering, in a medium bowl, combine the ricotta, eggs, oregano, 3/4 cup of the Parmesan, the remaining 1 1/2 teaspoons of salt, and the remaining 1 1/2 teaspoons of pepper.

Oil a 9-by-13-inch baking pan or a 3 1/2- to 4-quart casserole dish and spread a thin layer of the marinara mixture into the bottom. Top with 1/3 of the sweet potatoes, overlapping the slices slightly, 1/3 of the ricotta mixture, and 1/3 of the remaining marinara mixture. Repeat 2 more times. Top with the mozzarella and remaining 1/4 cup of Parmesan.

Cover loosely with foil and bake until heated through, 45 to 60 minutes.

Uncover and continue baking until the top is browned, 15 to 20 minutes. Let stand 10 minutes before serving.