Skillet Ziti with Chicken and Broccoli

This recipe originally came from America's Test Kitchen, but I got the recipe from Definitely RA.
I'd give this 3+ stars and it's entered our dinner rotation.

1 pound boneless, skinless chicken breasts sliced into 1-inch pieces
salt and pepper
3 tablespoons 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) (or penne or whatever other pasta you rustle up)
2 1/2 cups lo-sodium chicken broth
1/2 cup heavy cream
1 bunch broccoli (1 1/2 lbs), stems discarded and florets fut into 1 inch pieces (this seemed like a lot to me, but it might be because I was trying to convert from frozen florets)
1 cup jarred roasted red peppers, rinsed and sliced 1/4 inch thick (I was cheap and tried roasting my own red pepper on the grill - it worked great! I think I liked it better)
1 oz Parmesan cheese, grated (1/2 cup)
2 Tbsp fresh lemon juice (or, you know me, maybe more...)

1. Pat the chicken dry, then season with salt and pepper. Melt 1 Tbsp butter in 12 inch skillet (or, in my experience, bigger if you've got it) 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.

2. Add 1 more Tbsp butter, the onion, red pepper flakes, oregano, and 1/2 tsp of salt to the skillet. Cook until the onion is softened, about 5 minutes. Stir in the garlic and cook until fragrant, about 15 seconds.

3. Sprinkle the UNCOOKED ziti evenly into the skillet. Pour the broth and cream over the ziti. Cover and bring to a boil, about 5 minutes.

4. 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.

5. Stir in the chicken and any accumulated juice. Cover and continue to simmer until the chicken is cooked through, about 3 minutes longer.

6. Stir in the remaining 1 Tbsp. of butter, the Parmesan, and lemon juice. Season with salt and pepper to taste.