Bring a large pot of salted water to a boil and cook the penne until al dente according to package directions, about 10 to 11 minutes. Before draining, scoop out 1/2 cup of the starchy pasta water and set it aside. Drain the pasta and reserve.

Heat olive oil in a large skillet over medium-high heat. Season the diced chicken with salt, pepper, and paprika. Add to the hot pan in a single layer and sear for 5 to 6 minutes, turning once, until golden and cooked through to 165 degrees F internally. Remove and set aside on a plate.

Reduce the heat to medium and melt the butter in the same skillet. Add the chopped onion and minced garlic and cook for about 3 minutes until soft and fragrant. Keep a close eye on the garlic so it does not brown.

Add the broccoli florets and about 2 tablespoons of water. Cover the skillet and steam for 3 to 4 minutes until the broccoli is bright green and just tender-crisp. Do not overcook at this stage.

Reduce the heat to medium-low. Pour in the heavy cream and chicken broth and stir to combine. Simmer for 2 to 3 minutes until the sauce thickens slightly and coats the back of a spoon. Stir in the Parmesan until fully melted and creamy. If the sauce looks like it is separating, lower the heat and stir slowly to bring it back together.

Return the cooked chicken to the skillet and add the drained penne. Toss everything together until the pasta is well coated. Add the reserved pasta water a splash at a time if the sauce is too thick. Taste and adjust with salt, pepper, and red pepper flakes if using. Garnish with fresh parsley and serve immediately.