Preheat the oven to 350ºF.
Cook onions in 2 tablespoons olive oil in a large ovenproof skillet over medium heat, stirring often for 3 to 5 minutes. Reduce heat to low and cook slowly, stirring occasionally, to prevent browning, until onions are soft and sweet, 15 to 20 minutes more. Season with 1/4 teaspoon each salt and pepper. Remove skillet from heat and reserve onions and skillet.
Meanwhile, cook the pasta until just tender in a large pot of salted water according to package instructions. Drain and reserve.
Combine shredded cheddar, cottage cheese, milk, eggs, mustard, rosemary and 1/4 teaspoon each salt and pepper in a large mixing bowl. Add cooked pasta and caramelized onions, mixing to coat pasta and evenly distribute onions.
If needed, brush bottom and side of the same skillet (or a 2 quart baking dish if your skillet is not ovenproof) with additional olive oil and fill with the pasta mixture. Mix the breadcrumbs, Parmesan and remaining 1 tablespoon olive oil in a small bowl and sprinkle evenly over the top of the pasta. Cover with foil and bake in the preheated oven until beginning to bubble around the edges, 35 to 40 minutes. Remove foil and continue to bake 5 to 10 minutes until lightly browned.
Remove from oven and sprinkle with additional chopped rosemary, if desired.
Makes 4 to 6 servings.