Bring a pot of salted water to a boil and cook the 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 until tender-crisp.
While the pasta is cooking, season the chicken breast with sea salt and black pepper.
Heat olive oil in a 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 pan, let it rest for 2 minutes, then slice it into thin strips.
In the same skillet, reduce the heat to low and sauté the minced garlic for 30 seconds until fragrant.
Whisk in the Greek yogurt, parmesan cheese, and 2 tablespoons of the starchy pasta water to create a smooth, creamy sauce.
Drain the pasta and broccoli, then toss them into the skillet with the sauce and sliced chicken until well-coated.
Garnish with chopped fresh parsley and serve immediately.