In a large skillet or pan, heat olive oil over medium heat. Season the diced chicken with salt and pepper, then add it to the skillet. Cook for 5-7 minutes, stirring occasionally until the chicken is browned and cooked through.
Add the minced garlic to the skillet and sauté for an additional minute until fragrant.
Stir in the broccoli florets and cook for 2-3 minutes until they start to soften.
Pour in the uncooked penne pasta and chicken broth. Bring the mixture to a boil, then reduce the heat to low. Cover and let it simmer for 12-15 minutes, or until the pasta is cooked al dente and has absorbed most of the broth, stirring occasionally.
Once the pasta is cooked, remove the skillet from the heat. Stir in the shredded cheddar cheese and grated Parmesan cheese until melted and creamy.
Season with paprika, red pepper flakes (if using), and additional salt and pepper to taste.
Garnish with fresh parsley before serving.
Notes
Serve in deep bowls with extra cheese and broccoli for garnish.