Bring a medium pot of salted water to a boil and cook the chickpea pasta according to package directions, reserving 2 tablespoons of the cooking water before draining.
While the pasta cooks, season the chicken breast on both sides with sea salt, black pepper, and dried oregano.
Heat the olive oil in a large skillet over medium heat and cook the chicken for 5-7 minutes per side until golden brown and cooked through, then remove from the pan and let it rest.
Steam the broccoli florets in a steamer basket over boiling water for 3-4 minutes until they are bright green and tender-crisp.
In the same skillet used for the chicken, add the minced garlic and sauté for 30 seconds until fragrant, then turn the heat to low.
Whisk the Greek yogurt, parmesan cheese, and reserved pasta water into the skillet with the garlic until a smooth, creamy sauce forms.
Slice the rested chicken into strips and toss it into the skillet along with the cooked pasta and steamed broccoli, stirring gently to coat every ingredient in the sauce before serving.