Bring a large pot of salted water to a boil and cook the chickpea pasta according to package directions until al dente.
Place the broccoli florets in a steamer basket over the pasta pot for the last 3 minutes of cooking.
Reserve 2 tablespoons of the starchy pasta water, then drain the pasta and broccoli.
Season the chicken breast with sea salt and black pepper.
Heat the olive oil in a 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 skillet, let it rest for 3 minutes, then slice it into thin strips.
In the same skillet, reduce heat to low and sauté the minced garlic for 30 seconds until fragrant.
Whisk in the Greek yogurt, grated parmesan, and reserved pasta water to create a smooth, velvety sauce.
Toss the cooked pasta, steamed broccoli, and sliced chicken into the skillet until everything is well-coated in the sauce.
Garnish with freshly chopped parsley and serve immediately.