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 final 3 minutes of boiling.
While the pasta cooks, dice the chicken breast into small bite-sized pieces and season evenly with sea salt and black pepper.
Heat the olive oil in a large non-stick skillet over medium-high heat and sauté the chicken until golden and cooked through, approximately 5 to 7 minutes.
Reduce the skillet heat to medium, add the minced garlic, and sauté for 60 seconds until aromatic.
Reserve 2 tablespoons of the starchy pasta water, then drain the pasta and broccoli thoroughly.
In a small mixing bowl, whisk together the Greek yogurt, parmesan cheese, and the reserved pasta water until a smooth, creamy consistency is reached.
Transfer the cooked pasta and broccoli into the skillet with the chicken, then pour the yogurt sauce over the top.
Toss everything gently over low heat for 1 minute until the sauce is warmed through and coats the pasta, then garnish with fresh parsley and serve immediately.