Bring a large pot of salted water to a boil and cook the whole wheat penne according to package directions, adding the broccoli florets during the last 3 minutes of cooking.
While the pasta cooks, slice the chicken breast into bite-sized pieces and season with sea salt and black pepper.
Heat the ghee in a large skillet over medium-high heat and sauté the chicken until golden brown and cooked through, about 5-7 minutes.
Add the minced garlic to the skillet and cook for 1 minute until fragrant, then reduce the heat to low.
Drain the pasta and broccoli, reserving about 2 tablespoons of the starchy cooking water.
In a small bowl, whisk the Greek yogurt and parmesan cheese together until smooth.
Add the cooked pasta, broccoli, and yogurt mixture to the skillet with the chicken, tossing gently and adding reserved pasta water as needed to create a creamy sauce.
Serve immediately while warm and creamy.