Bring a pot of salted water to a boil and cook the whole wheat pasta according to package directions, reserving 2 tablespoons of pasta water before draining.
While the pasta cooks, season the chicken breast with half of the sea salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat and sear the chicken until golden and cooked through, about 5-6 minutes per side, then set aside to rest before slicing.
In the same skillet, add the broccoli florets and a splash of water; cover and steam for 3 minutes until bright green and tender-crisp.
Lower the heat to medium-low, add the minced garlic to the skillet, and sauté for 1 minute until fragrant.
In a small bowl, whisk together the Greek yogurt, parmesan cheese, and the reserved pasta water until smooth.
Add the cooked pasta and sliced chicken back into the skillet with the broccoli.
Pour the yogurt sauce over the mixture and toss gently to coat, ensuring the heat is low so the yogurt doesn't curdle.
Garnish with fresh chopped parsley and the remaining sea salt and pepper before serving.