Bring a pot of salted water to a boil and cook the whole wheat pasta according to package directions, adding the broccoli florets during the last 3 minutes of cooking.
Reserve 2 tablespoons of the pasta cooking water, then drain the pasta and broccoli.
While pasta cooks, season the chicken breast with half the salt and pepper.
Heat olive oil in a skillet over medium heat and cook the chicken until golden brown and cooked through, about 5-6 minutes per side.
Remove chicken from the pan, let it rest for 2 minutes, then slice into thin strips.
In the same skillet, reduce heat to low and add minced garlic, sautéing for 30 seconds until fragrant.
Whisk in the Greek yogurt, Parmesan cheese, remaining salt, pepper, and the reserved pasta water until a smooth, velvety sauce forms.
Add the cooked pasta, broccoli, and chicken back into the skillet, tossing gently to coat every ingredient in the sauce.
Garnish with fresh chopped parsley and serve immediately.