Preheat oven to 400°F and line a baking sheet with parchment paper.
Toss the broccoli florets and sliced red bell peppers with olive oil, sea salt, and black pepper on the prepared sheet.
Roast the vegetables for 15-20 minutes until they are tender and show slight caramelized edges.
While vegetables roast, boil the chickpea pasta according to package directions, reserving 2 tablespoons of pasta water before draining.
Season the chicken breast with a pinch of salt and pepper, then pan-sear in a non-stick skillet over medium heat until cooked through, about 6 minutes per side.
In a small bowl, whisk together the Greek yogurt, grated parmesan, and minced garlic until combined.
Slice the cooked chicken into bite-sized strips.
In the pasta pot over very low heat, combine the drained pasta, yogurt mixture, and reserved pasta water, stirring gently until a creamy sauce forms.
Fold in the roasted vegetables and sliced chicken, then garnish with fresh parsley before serving.