Start your chicken nuggets by putting the cooked chicken and the onion in the food processor until the chicken is shredded (but not paste). Then add the mayo and egg and cheese to the processor and blend until mixed together. Form the mixture into small shapes and coat with the bread crumbs.
Bake the homemade chicken nuggets at 400F for 18 or so minutes, turning halfway. Just long enough to cook the egg and to stick together.