Heat 1 tablespoon of olive oil in a large, oven-safe sauté pan over medium-high heat. Add the sausages and sear, turning frequently, for about 5 minutes or until browned on all sides.
Remove the sausages to a plate and set aside. Add the onion, celery, and carrot to the skillet and sprinkle lightly with salt and pepper. Cook for 4 minutes or until the onion is lightly browned. Add the tomato paste, garlic, and Italian seasoning; cook, stirring, for 2 minutes.
Meanwhile, pour 2 cups of water into a saucepan and boil over high heat. Pour the boiling water over the vegetables in the sauté pan. Add the spaghetti and stir to blend. Taste and season with salt and pepper as needed. Place the sausages on the spaghetti mixture and bring to a simmer. Cover the pan and transfer it to the oven.
Bake the spaghetti for 25 to 30 minutes or until all the water is absorbed. Remove the pan to a rack and set the oven to broil. In a small bowl, combine the Parmesan cheese, breadcrumbs, and chopped parsley. Toss with the remaining 1 tablespoon of olive oil.
Sprinkle the breadcrumb mixture over the spaghetti and place the pan under the broiler for about 3 minutes or until the topping crumbs are crisp and golden brown.