Linguine with hot italian sausages

For the sauce:
2 tablespoons extra-virgin olive oil
1/2 medium yellow onion, finely chopped
2 medium garlic cloves, thinly sliced
1/4 cup shredded carrot
1 teaspoon dried oregano
1 can (28 ounces) peeled whole tomatoes
1/2 teaspoon kosher salt
1/4 teaspoon freshly ground black pepper
4 hot Italian sausages, about 4 ounces each and 1 inch thick
1/4 cup finely chopped fresh basil
1 pound linguine
1 cup toasted breadcrumbs (optional)

1. To make the sauce: In a medium saucepan, heat the olive oil over medium heat. Add the onion and garlic. Cook for 5 minutes, stirring occasionally. Add the carrot and oregano. Cook for 5 more minutes, stirring occasionally. In a large bowl crush the tomatoes in your hands and add them, along with all the juices, to the saucepan. Season with the salt and pepper. Simmer for 10 minutes.
2. Grill the sausages over Direct Medium heat until no longer pink in the center, 6 to 10 minutes, turning once halfway through grilling time. Remove the sausages from the grill. Slice them thinly crosswise and then roughly chop them. Add the sausages and basil to the saucepan. Stir. Keep warm.
3. In a large pot of boiling salted water, cook the linguine until barely tender. Drain the linguine and return it to the pot. Add the sauce. Stir to combine. Cover the pot for 1 minute to allow the pasta to absorb some sauce. Sprinkle toasted breadcrumbs on top, if desired. Serve warm.