Bring a large pot of salted water to a boil.
Cook penne until al dente. Reserve 1/2 cup pasta water, then drain and set aside.
Pat chicken dry. Season with 1/2 teaspoon salt and the black pepper.
Heat olive oil in a large skillet over medium-high heat until shimmering.
Sear chicken until browned and cooked through, 4–6 minutes. Transfer to a plate to rest.
Lower heat to medium. Soften diced onion in the same skillet, 3–4 minutes.
Stir in garlic and tomato paste. Cook until fragrant and darkened slightly, about 1 minute.
Add Italian seasoning and red pepper flakes. Toast 30 seconds, stirring.
Add roasted red peppers and chicken broth. Simmer until slightly reduced, 3–4 minutes.
Pour in heavy cream. Return chicken and any juices to the pan; warm through gently.
Fold in cooked penne and spinach. Stir until spinach wilts.
Stir in Parmesan. Loosen the sauce with splashes of reserved pasta water as needed.
Finish with lemon juice and remaining salt to taste. Sprinkle with parsley or basil.