Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
In a food processor, combine the chickpeas, egg whites, fresh parsley, ground cumin, garlic powder, salt, and pepper. Pulse until the mixture holds together but still has some texture.
Scoop the mixture into small patties, shaping them into rounds about the size of your palm. Place the patties onto the prepared baking sheet.
Bake in the preheated oven for 20-25 minutes, flipping halfway through, until the falafel patties become firm and lightly golden. For extra crispiness, you can broil for an additional 2-3 minutes at the end.
Warm your whole wheat wrap lightly in a pan or microwave.
Spread the hummus over the wrap, then layer on the baked falafel patties.
Add sliced red bell pepper and sprinkle crumbled feta cheese over the top.
Roll up the wrap tightly, slice in half if desired, and serve immediately.