Heat olive oil in a large deep skillet over medium-high heat. Add chicken, sear without moving for 4 minutes, then stir and cook 2-3 minutes more until browned and just cooked through. Transfer to a plate.

Reduce heat to medium, add onion, and cook 3 minutes until softened. Add garlic and red pepper flakes, cook 30 seconds until fragrant.

Pour in broth and tomatoes, scrape up browned bits, then add penne. Bring to a boil, cover, reduce heat, and simmer 12-14 minutes, stirring once, until pasta is tender and liquid is mostly absorbed.

Turn heat to low, stir in heavy cream, then add spinach by handfuls until wilted. Return chicken and juices to pan, cook 2 minutes to warm through. Season with salt and pepper.

Toss everything together, spoon into bowls, and top with Parmesan. Serve immediately.