Bring a large 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 boiling water to steam them alongside the noodles.
Reserve 0.25 cup of the starchy pasta water, then drain the pasta and broccoli.
Season the chicken breast with sea salt, black pepper, and garlic powder.
Heat olive oil in a skillet over medium heat and sear the chicken for 5-6 minutes per side until fully cooked, then slice into strips.
In the same skillet, reduce heat to low and sauté the minced garlic for 30 seconds until fragrant.
Whisk together the Greek yogurt, parmesan cheese, and the reserved pasta water in the skillet until a smooth, creamy sauce forms.
Add the cooked pasta, broccoli, and chicken back into the skillet, tossing gently to coat everything in the velvety sauce before serving.