Cut chicken breasts in half horizontally to create thinner cutlets. This helps them cook evenly and quickly. Season both sides generously with salt, pepper, and half of the Italian seasoning.
Heat olive oil in a large, deep skillet over medium-high heat until it shimmers. Add chicken and cook for 4-5 minutes per side until golden brown with nice caramelized spots. The chicken should release easily from the pan when it’s ready to flip. Transfer to a plate – it’s okay if it’s not fully cooked through yet.
In the same pan (don’t wipe it out – those browned bits add flavor!), add butter and minced garlic. Cook for about 30 seconds, until the garlic becomes fragrant but not brown. Add sun-dried tomatoes and stir for another minute.
Add the uncooked penne, remaining Italian seasoning, red pepper flakes, and chicken broth. Give it a good stir and bring to a boil. Reduce heat to medium-low, cover, and simmer for 8-10 minutes, stirring occasionally to prevent sticking. You’ll know the pasta is almost done when it’s just slightly firmer than you’d like to eat.
Pour in the heavy cream and return chicken to the pan, nestling it into the pasta. Cover and cook for another 3-4 minutes until the chicken is cooked through (cut into the thickest part – it should be completely white inside) and the pasta is al dente.
Add the fresh spinach in handfuls, stirring until it wilts into the sauce. This usually takes about 2 minutes. The leaves should be bright green and just softened.
Finally, stir in the Parmesan cheese until it melts completely and the sauce turns silky smooth. If the sauce seems too thick, add a splash of broth or cream. If too thin, let it simmer uncovered for a minute or two.