Preheat the oven to 400 degrees F. Grease a sheet pan with non-stick cooking spray.
In the bowl of a food processor, combine the chickpeas, garlic, onions, cilantro, parsley, cumin, cayenne, salt, pepper, flour and baking powder. Process the mixture until it resembles coarse breadcrumbs and with the motor running, drizzle in the olive oil.
Form the mixture into 12 equal-sized patties and place on the prepared sheet pan. Bake the falafel for 25-30 minutes, turning halfway, until both sides are golden brown.
While the falafel is baking, make the dressing. In a small bowl, combine the lemon juice, hummus, salt and pepper. Whisk in the olive oil until fully combined.
To assemble the salad, toss the Romaine, carrots, tomatoes, cucumber and Feta in the dressing and top with falafel.Serve with pita.