Cook the pasta according to package instructions until al dente. During the last 2 minutes of cooking, add broccoli florets to the pot to blanch. Drain and set aside.
Heat olive oil in a large skillet over medium heat. Add diced chicken, season with salt and pepper, and cook for 6-7 minutes, or until golden and cooked through. Remove chicken and set aside.
In the same skillet, add minced garlic and sauté for 1 minute until fragrant.
Pour in the heavy cream and bring to a gentle simmer. Stir in Parmesan cheese until melted and the sauce is creamy.
Add the cooked pasta, broccoli, and chicken back to the skillet, tossing to combine. Season with additional salt and pepper if needed.