Heat oil in a large nonstick lidded skillet over medium-high heat. Season beef with 1/4 teaspoon of the salt. Add to skillet and cook for 2 minutes. Turn and cook for an additional 2 minutes. Remove beef from skillet to a plate with a slotted spoon. Keep warm.
Add onion and celery to skillet and cook, stirring occasionally, for 5 minutes. Add garlic and cook for 1 minute. Stir in tomatoes, beans, oregano, basil, red pepper flakes and remaining 1/2 teaspoon salt. Bring to a boil. Reduce heat to medium-low and simmer, covered, for 12 minutes. Stir occasionally.
Meanwhile, cook pasta following package directions, about 8 minutes. Drain, reserving 1 cup of the cooking water. Place drained pasta back into pot. Add the bean mixture, cooked beef with accumulated juices and the reserved cooking water to the pasta.
Serve with grated cheese, if desired.