Put beans, carrots, and garlic in a food processor and chop. Add remaining ingredients and stir. Grease a jelly roll or similar pan. Form falafel into half-dollar-sized patties and place on pan. Brush olive oil on top of falafel. Bake at 425 degrees 10-14 minutes, turning once. (I generally do 7 minutes on each side, but the original recipe says 10 minutes.)
Serve on pitas with vegetables and a yogurt dip of your choice.