Heat 2 tablespoons extra-virgin olive oil in a large skillet over medium-high heat.
Season both sides of the chicken breasts with salt and pepper (and garlic salt if desired).
Add the chicken to the hot skillet and cook until browned and cooked through, about 7–8 minutes per side; transfer to a cutting board and let rest 10 minutes.
Slice the rested chicken into strips or bite-sized pieces and set aside.
In the same skillet, add the milk, chicken broth, and 2 teaspoons minced garlic; season with salt and pepper, then bring to a simmer while scraping up any browned bits.
Stir in the dry penne and the broccoli florets, ensuring the pasta is submerged; cook, stirring often, for about 3 minutes, then continue cooking and stirring for an additional 8 minutes until pasta is tender.
Reduce heat to medium-low, then stir in 1/2 cup heavy cream and 1 cup freshly grated Parmesan until the cheese melts and the sauce thickens, simmering a few minutes more.
Add the sliced chicken back to the skillet and stir to combine and heat through.
Serve immediately, garnished with chopped parsley and additional Parmesan if desired.
