Skillet Ziti With Chicken & Broccoli

1 pound boneless, skinless chicken breast, sliced into 1" pieces
Salt and pepper
3 Tablespoons unsalted butter
1 onion, minced (we omitted this due to personal tastes)
1/4 teaspoon red pepper flakes
1/4 teaspoon dried oregano
3 garlic cloves, minced
8 ounces ziti (2 1/2 cups)
2 1/2 cups low-sodium chicken broth
1/2 cup heavy cream (I substituted this with half & half)
1 bunch broccoli (1 1/2 pounds)
1 cup jarred roasted red peppers, rinsed and sliced 1/4" thick
1 ounce Parmesan cheese, grated (1/2 cup)
2 tablespoons fresh lemon juice (optional)

Pat the chicken dry, then season with salt and pepper. Melt 1 tablespoon of the butter in a 12" skillet over medium heat. Add the chicken and cook until it is lightly browned, but not fully cooked, about four minutes. Transfer chicken to a bowl. Add 1 more tablespoon of the butter, onion, red pepper flakes, oregano, & 1/2 teaspoon salt to the skillet. Cook until the onion is softened, about five minutes. Stir in the garlic and 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 five minutes. Reduce the heat to medium-low and stir in the broccoli and roasted red peppers. Cover and continue to simmer, stirring occasionally, until the pasta begins to soften and the broccoli turns bright green (approximately eight minutes). Stir in the chicken and any accumulated juice. Cover and simmer until the chicken is cooked through, about three minutes longer. Stir in the remaining 1 tablespoon butter, the Parmesan, and lemon juice (if using). Season with salt and pepper to taste.