Steam broccoli and carrots, drain and finely chop. Place broccoli mixture and flour in a large bowl; stir to coat. Add cheese, salt, pepper, onions,and egg to broccoli mixture. Stir to combine. Heat a large nonstick skillet over medium heat. Add oil to pan and coat. Form small patties with mixture in the palm of your hand and flatten slightly until all of the mixture is gone (about 10 patties). Cook 4 minutes on each side or until golden brown. Serve with dipping sauce and fresh fruit.