Bring a large pot of salted water to a boil and cook the chickpea penne according to package instructions, adding the broccoli florets during the final 3 minutes of boiling.
While the pasta cooks, season the chicken breast with sea salt and black pepper.
Heat the olive oil in a medium skillet over medium-high heat and cook the chicken until golden brown and cooked through, approximately 5 to 7 minutes per side.
Transfer the chicken to a cutting board, allow it to rest for 2 minutes, then slice into thin strips.
In a small mixing bowl, whisk together the Greek yogurt, grated parmesan cheese, minced garlic, and lemon juice until smooth.
Drain the pasta and broccoli, reserving 2 tablespoons of the hot cooking water.
Return the pasta and broccoli to the pot over low heat, then stir in the yogurt mixture and the reserved pasta water to create a creamy consistency.
Add the sliced chicken to the pot and toss gently to coat everything in the sauce.
Serve immediately garnished with freshly chopped parsley.