Bring a large pot of salted water to a boil and cook the whole wheat fettuccine according to package directions until al dente.
While the pasta cooks, season the chicken breast with half of the sea salt and black pepper.
Heat the olive oil in a skillet over medium-high heat and sear the chicken for 5-6 minutes per side until cooked through, then set aside to rest before slicing.
Steam the broccoli florets in a steamer basket or microwave with a splash of water until tender-crisp.
In the same skillet used for the chicken, reduce heat to low and sauté the minced garlic for 30 seconds until fragrant.
Whisk together the Greek yogurt, grated parmesan, remaining salt, pepper, and 2 tablespoons of the hot pasta water in a small bowl.
Drain the pasta and return it to the skillet, tossing with the yogurt sauce, steamed broccoli, and sliced chicken.
Garnish with fresh chopped parsley and serve immediately.