Bring a large pot of generously salted water to a rolling boil. Cook the penne 1 minute shy of the package directions for al dente. Before draining, scoop out 1 cup of the starchy pasta water, then drain the pasta.

While the water heats, pat the chicken strips dry and season with 1/2 teaspoon of the salt, the black pepper, and the Italian seasoning. Heat the olive oil in the large skillet over medium-high heat. Sear the chicken in a single layer, turning once, until deeply golden and cooked through to 165°F, about 5–6 minutes. Transfer to a plate.

Reduce the heat to medium. Add the chopped sun-dried tomatoes, garlic, tomato paste, and red pepper flakes (if using) to the same skillet. Cook, stirring constantly, until the tomato paste darkens a shade and smells sweet, about 2 minutes.

Pour in the chicken broth, scraping up every browned bit from the bottom of the skillet. Stir in the heavy cream and the remaining 1/2 teaspoon salt. Bring to a gentle simmer and cook 2–3 minutes, until the sauce thickens just enough to coat the back of a spoon.

Add the drained penne and the seared chicken (with any resting juices) back to the skillet. Sprinkle in the Parmesan and toss with tongs, loosening with splashes of the reserved pasta water, until every tube of penne is glossed with pink sauce.

Fold in the torn basil. Divide among warm bowls and finish with extra Parmesan, cracked black pepper, and more basil.