Skillet Chicken with Broccoli, Pasta, and Parmesan Cheese (Jean)

2-3 boneless, skinless chicken breasts, cut into 1-inch squares
Table salt and ground black pepper
3 tablespoons olive oil
1 medium onion, minced
4 medium cloves garlic, minced
1/2 teaspoon dried oregano
1/4 teaspoon red pepper flakes
12 ounces ziti (penne makes a great substitution - I've used both with great results)
4 1/4 cups water
2 1/2 cups low-sodium chicken broth
4-5 cups broccoli florets (depending on how much broccoli you want)
1/2 cup oil-packed sun-dried tomatoes, rinsed and chopped coarse
3/4 cup heavy cream
3/4 cup grated parmesan cheese (asiago was the cheese in the original recipe and can be interchanged, but I always have parmesan on hand so I used that)
1 1/2 tablespoons fresh lemon juice

Season the chicken with salt and pepper. Heat 2 tablespoons of the oil in a 12-inch nonstick skillet over medium-high heat until just smoking. Add the chicken in a single layer and cook for 1 minute without stirring. Stir the chicken and continue to cook until most, but not all, of the pink color has disappeared and the chicken is lightly browned around the edges, 1 to 2 minutes longer. Transfer the chicken to a clean bowl and set aside.

Add the remaining tablespoon of oil, onion, and 1/2 teaspoon salt to the skillet. Return the skillet to medium-high heat and cook, stirring often, until the onion is softened, 2 to 5 minutes. Stir in the garlic, oregano, and pepper flakes, and cook until fragrant, about 30 seconds.

Add the pasta, 3 cups of the water, and the broth. Bring to a boil over high heat and cook until the liquid is very thick and syrupy and almost completely absorbed, 12 to 15 minutes, stirring occasionally.

Add the broccoli, sun-dried tomatoes, and the remaining 1 1/4 cups water. Cover, reduce the heat to medium, and cook until the broccoli turns bright green and is almost tender, 2-3 minutes.

Uncover and return the heat to medium-high. Stir in the cream, parmesan, and reserved chicken with any accumulated juices and continue to simmer, uncovered, until the sauce is thickened and the chicken is cooked and heated through, 1 to 2 minutes. Off the heat, stir in the lemon juice and season with salt and pepper to taste. Serve, passing more grated parmesan at the table, if desired.