Bring a large pot of salted water to a boil and cook the whole wheat fettuccine according to package directions until al dente.
During the last 3 minutes of pasta cooking, add the broccoli florets to the same pot to steam them until tender-crisp, then drain everything and set aside.
Season the chicken breast with sea salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat and sear the chicken until golden brown and cooked through, about 5-6 minutes per side.
Remove the chicken from the skillet, let it rest for 2 minutes, then slice it into thin strips.
In the same skillet, reduce heat to low and add the minced garlic, sautéing for 30 seconds until fragrant.
Whisk together the Greek yogurt, chicken broth, and parmesan cheese in a small bowl, then pour the mixture into the skillet with the garlic.
Stir the sauce constantly over low heat until the cheese is melted and the sauce is smooth, being careful not to let it boil.
Add the cooked pasta, broccoli, and sliced chicken back into the skillet and toss well to coat everything in the creamy sauce.
Garnish with fresh parsley and serve immediately.