Preheat your oven to 400°F and line a baking sheet with parchment paper.
Place the broccoli florets on the baking sheet, drizzle with half of the olive oil, and season with a pinch of salt and pepper.
Roast the broccoli for 15-18 minutes until the edges are slightly charred and tender.
While broccoli roasts, bring a pot of salted water to a boil and cook the fettuccine according to package instructions, reserving 0.25 cup of pasta water before draining.
Season the chicken breast with the remaining salt and pepper, then sear in a pan with the remaining olive oil over medium-high heat for 5-6 minutes per side until cooked through.
Remove chicken from the pan, let it rest for 2 minutes, then slice into thin strips.
In the same pan over low heat, add the minced garlic and sauté for 30 seconds until fragrant.
Whisk in the Greek yogurt, parmesan cheese, and the reserved pasta water until a smooth, creamy sauce forms.
Add the cooked pasta, roasted broccoli, and sliced chicken to the pan, tossing gently to coat everything in the sauce.
Garnish with freshly chopped parsley and serve immediately.