Season chicken pieces with 1/2 tsp salt and 1/4 tsp pepper. Heat olive oil in a large deep skillet or Dutch oven over medium-high heat. Add chicken in a single layer and cook for 3–4 minutes per side until golden and cooked through (internal temperature of 165°F/74°C). Transfer to a plate.

Reduce heat to medium-low. Add minced garlic and red pepper flakes (if using) to the same pot. Sauté for 30–60 seconds until fragrant, stirring constantly to prevent burning.

Pour in chicken broth and heavy cream, scraping up any browned bits. Add penne pasta, remaining 1/2 tsp salt, and remaining 1/4 tsp pepper. Stir to combine and bring to a boil.

Once boiling, reduce heat to medium-low, cover, and simmer for 12–15 minutes, stirring occasionally, until pasta is al dente and most liquid is absorbed.

Remove from heat. Fold in spinach, Parmesan, and the cooked chicken. The spinach will wilt in the residual heat. Taste and adjust salt and pepper.

Spoon into bowls, garnish with parsley and extra Parmesan. Serve immediately.