Step 1: Prepare the pasta.
Start by bringing a large pot of salted water to a boil. Once the water is boiling, add the pasta and cook according to the package instructions, usually for about 8-10 minutes, until al dente. Drain the pasta and set it aside.

Step 2: Cook the chicken.
While the pasta is cooking, heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Season the chicken breasts with salt and pepper. Place the chicken in the skillet and cook for about 6-8 minutes per side, or until fully cooked and no longer pink inside. Remove the chicken from the skillet and let it rest for a few minutes before slicing it into thin strips or bite-sized pieces.

Step 3: Cook the broccoli.
In the same skillet, add another tablespoon of olive oil if necessary. Add the broccoli florets and sauté for about 4-5 minutes, until they become tender but still crisp. If you prefer, you can blanch the broccoli in boiling water for 2-3 minutes instead.

Step 4: Prepare the Alfredo sauce.
To make the creamy Alfredo sauce, reduce the heat to medium-low in the skillet. Add butter and minced garlic to the skillet, cooking for about 1 minute until fragrant. Pour in the heavy cream and bring it to a gentle simmer. Stir in the grated Parmesan cheese and mozzarella (if using), and continue stirring until the sauce thickens, about 3-5 minutes. Add salt, pepper, and Italian seasoning to taste.

Step 5: Combine everything.
Add the cooked pasta, broccoli, and sliced chicken into the skillet with the Alfredo sauce. Toss everything together until evenly coated. Adjust the seasoning with additional salt and pepper, if needed.