Bring a pot of salted water to a boil and cook the penne pasta according to package directions until al dente.
During the last 3 minutes of pasta cooking, add the broccoli florets to the same pot to blanch them until bright green.
Before draining, carefully reserve 2 tablespoons of the starchy pasta water, then drain the pasta and broccoli.
While pasta cooks, season the chicken breast with sea salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat and sear the chicken for 5-6 minutes per side until fully cooked and golden brown.
Remove the chicken from the pan, let it rest for 2 minutes, then slice into strips.
Reduce the skillet heat to low, add the minced garlic, and sauté for 30 seconds until fragrant.
In a small bowl, whisk together the Greek yogurt, parmesan cheese, and the reserved pasta water to create a smooth sauce base.
Add the cooked pasta, broccoli, and sliced chicken back into the skillet.
Pour the yogurt sauce over the mixture and toss gently on low heat just until the sauce is warm and coats everything evenly.
Garnish with fresh chopped parsley and serve immediately.