Preheat the oven to 375°F (190°C).
Bring a large pot of salted water to a boil and cook the jumbo shells according to package directions until al dente; drain and rinse under cold water to stop cooking, then set aside to cool.
Meanwhile, heat the olive oil in a skillet over medium heat and cook the finely chopped onion until softened, about 3–5 minutes; remove from heat and let cool slightly.
In a food processor, purée the cottage cheese until smooth, then transfer to a large bowl.
Add the breadcrumbs, nutmeg, and 1/2 cup of the grated Parmesan to the cottage cheese and mix until combined.
Stir the cooked onions and the well-drained chopped spinach into the cheese mixture, season with salt and pepper, then fold in the lightly beaten egg white.
Spoon about 2 tablespoons of the cheese and spinach mixture into each cooked shell.
Spread 1 cup of marinara sauce across the bottom of a 9x13-inch baking dish, arrange the stuffed shells in a single layer over the sauce, then spoon the remaining 2 cups of marinara sauce over the shells and sprinkle with the remaining 1/4 cup of Parmesan.
Bake uncovered at 375°F for about 30 minutes, until heated through and the cheese is golden; tent loosely with foil if the top browns too quickly.
Let the casserole cool for 10 minutes before serving.