Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Place the sliced zucchini and chopped bell peppers on the baking sheet, drizzle with olive oil, and toss to coat before roasting for 20 minutes.
While the vegetables roast, combine the rinsed chickpeas, egg whites, parsley, cumin, garlic powder, salt, and pepper in a food processor.
Pulse the mixture until a coarse paste forms, being careful not to over-process into a smooth purée.
Form the chickpea mixture into 6 small patties and place them on a second parchment-lined baking sheet.
Bake the falafel for 15-18 minutes, flipping once halfway through, until the exterior is golden and crispy.
In a small bowl, whisk together the Greek yogurt, tahini, and lemon juice until the sauce is smooth and creamy.
Plate the roasted vegetables, top with the falafel patties, and drizzle the yogurt sauce over the entire dish.