Bring a large pot of salted water to a boil and cook the fettuccine according to package instructions until al dente.
While pasta cooks, add the broccoli florets to a steamer basket over the pasta water for the last 3 minutes of cooking until tender-crisp.
Season the chicken breast with sea salt and black pepper.
Heat olive oil in a large skillet over medium-high heat and sauté the chicken until golden brown and cooked through, about 5-6 minutes per side.
Remove chicken from the pan, let it rest for a few minutes, then slice into strips.
In the same skillet, reduce heat to medium and add minced garlic, cooking for 1 minute until fragrant.
Whisk in the chicken broth, scraping up any browned bits from the bottom of the pan.
Remove skillet from heat and whisk in the Greek yogurt and parmesan cheese until a smooth, creamy sauce forms.
Add the cooked pasta, steamed broccoli, and sliced chicken back into the skillet, tossing gently to coat everything in the sauce.
Garnish with fresh parsley and serve immediately.