Bring a large pot of salted water to a boil and cook the penne according to the package directions until al dente; drain and set aside.
In a large skillet over medium heat, combine the jarred pasta sauce, pressed garlic, and red pepper flakes. Heat until the sauce is bubbling and fragrant, about 3–5 minutes.
Add the cottage cheese and stir until incorporated and the sauce is hot.
Stir in the cooked chicken and cook until the chicken is heated through.
Add the cooked penne to the skillet and toss with the sauce, then stir in the shredded mozzarella until melted and evenly distributed; taste and season with salt and pepper if desired.
Serve hot, optionally topped with grated Parmesan.
Notes
Banza chickpea pasta is a good low-carb substitute.
Use meal-prep chicken, Instant Pot chicken, or rotisserie chicken for convenience.
To start with raw chicken: cut into bite-sized pieces, season, and brown in oil before adding sauce and finishing as directed.