Pat the chicken dry, then season with salt and pepper. Melt 1 tablespook of the butter in a 12 inch skillet over medium-high heat. Add the chicken and cook until it is lightly browned but not fully cooked, about 4 minutes. Transfer the chicken to a bowl.
Reduce heat to medium. Add 1 more tablespoon of the butter, onion, red peppers, red pepper flakes, oregano and the 1/2 tsp salt to the skillet. Cook until onion is softened, about 5 minutes. Stir in the garlic and cook until fragrant, about 15 seconds.
Sprinkle the penne (uncooked) evenly into the skillet. Pour the broth and cream over the ziti. Cover and bring to a boil, about 5 minutes.
Reduce the heat to medium-low and stir in the broccoli. Cover and continue to simmer, stirring occasionally, until the pasta begins to soften and the broccoli turns bright green, about 8 minutes.
Stir in the chicken and any accumulated juices. Cover and continue to simmer until the chicken is cooked through, about 3 minutes.
Stir in the remaining 1 tbsp butter and the parmesan. Season with salt and pepper to taste.