Cook penne in a large pot of water with the tablespoon salt until 1 minute short of the package time. Reserve 1 cup pasta water before draining.
Meanwhile, season chicken with its salt and pepper. Heat oil in a large skillet and cook chicken for 6 to 8 minutes, turning, until browned and at least 165°F; transfer to a plate.
Lower heat to medium and stir garlic, sun-dried tomatoes and tomato paste in the skillet for 1 minute. Add broth, cream, oregano and crushed red pepper and simmer gently for 4 minutes.
Add penne, chicken and 1/4 cup reserved pasta water and toss over low heat for 1 to 2 minutes until the pasta is tender.
Remove from heat and stir in Parmesan, adding more pasta water a tablespoon at a time if needed for a smooth coating. Serve promptly.