Bring a pot of water to a boil and cook the chickpea pasta according to package directions until al dente.
During the last 3 minutes of pasta cooking, add the broccoli florets to the pot to blanch them until tender-crisp.
While pasta cooks, heat olive oil in a large skillet over medium-high heat and add the diced chicken breast seasoned with sea salt, black pepper, and dried oregano.
Sauté the chicken for 5 to 7 minutes until golden brown and cooked through, then add the minced garlic for the final minute of cooking.
In a small bowl, whisk together the Greek yogurt, lemon juice, and lemon zest until the mixture is smooth.
Drain the pasta and broccoli, reserving 2 tablespoons of the pasta cooking water.
Turn the skillet heat to low, then add the pasta, broccoli, yogurt mixture, and reserved water to the chicken.
Toss everything gently until a creamy sauce forms and coats the pasta, then garnish with fresh parsley before serving.