Bring a large pot of salted water to a boil and cook the whole wheat fettuccine according to package directions until al dente.
While pasta cooks, season the chicken breast with half of the sea salt and black pepper.
Heat the extra virgin 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.
Remove the chicken from the skillet, let it rest for a few minutes, then slice into thin strips.
In the same skillet, add the minced garlic and sauté for 30 seconds until fragrant, then add the broccoli florets and a splash of water to steam for 2 minutes.
In a small bowl, whisk together the Greek yogurt, grated Parmesan, and remaining salt and pepper.
Drain the pasta, reserving 2 tablespoons of the starchy pasta water.
Reduce the skillet heat to low, add the pasta, sliced chicken, yogurt mixture, and reserved pasta water to the pan.
Toss everything together gently until the sauce becomes velvety and coats the noodles evenly.
Garnish with fresh chopped parsley before serving.