Bring a large pot of salted water to a boil. Add penne and cook according to package instructions. In the last 3-4 minutes of cooking, add the broccoli florets to the pot. Drain and set aside.

While pasta cooks, season chicken pieces with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Add chicken and cook until golden brown and cooked through (5-7 minutes). Remove from skillet and set aside.

In the same skillet, melt butter over medium heat. Add minced garlic and cook until fragrant, about 30 seconds. Pour in chicken broth to deglaze, scraping any bits from the bottom. Stir in heavy cream and bring to a simmer for 2-3 minutes to thicken.

Reduce heat to low and stir in the grated Parmesan cheese until melted and the sauce is smooth. Season with salt, pepper, and optional red pepper flakes. Return the cooked chicken to the skillet, then add the drained pasta and broccoli.

Toss everything together until well-coated and heated through. Serve immediately, garnished with extra Parmesan cheese.