Bring a large pot of salted water to a boil and cook the 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 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 pan, let it rest for 3 minutes, then slice into thin strips.
In the same skillet, reduce the heat to low and sauté the minced garlic for 1 minute until fragrant.
In a small bowl, whisk together the Greek yogurt, chicken broth, and parmesan cheese, then add the mixture to the skillet.
Stir the sauce constantly on low heat until warmed through, ensuring it does not reach a boil to maintain a smooth texture.
Toss the cooked fettuccine and sliced chicken into the skillet, adding a splash of pasta water if needed to reach your desired creaminess.
Garnish with fresh parsley and the remaining salt and pepper before serving.