Skillet Ziti with Chicken and Broccoli

This recipe is courtesy America's Test Kitchen

1 pound boneless, skinless chicken breasts, slice into 1-inch pieces
Salt and pepper
3 Tbsp unsalted butter
1 onion, minced
1/4 tsp red pepper flakes
1/4 tsp dried oregano
3 garlic cloves, minced
8 ounces ziti
2 1/2 cups low-sodium chicken broth
1/2 cup heavy cream
1 bunch broccoli, stems discarded and florets cut into 1 inch pieces
1 cup jarred roasted red peppers, rinsed and sliced 1/4 inch thick (I left these out)
1 ounce Parmesan cheese, grated (1/2 cup)
2 Tbsp fresh lemon juice (optional)

Pat the chicken dry, then season with salt and pepper. Melt 1 Tbsp of the butter in a skillet over medium heat. Add the chicken and cook until it is lightly browned but not fully cooked, about 4 minutes. Transfer the chicken to a bowl.
Add 1 more Tbsp of the butter, onion, red pepper flakes, oregano, and 1/2 tsp salt to the skillet. Cook until the onion is softened, about 5 minutes. Stir in the garlic ande cook until fragrant, about 15 seconds.
Sprinkle the ziti 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 and roasted peppers. 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 juice. Cover and continue to simmer until the chicken is cooked through, about 3 minutes longer.
Stir in the remaining 1 Tbsp butter, the Parmesan, and lemon juice. Season with salt and pepper to taste.