In a large bowl combine the ground ham, onion, broccoli and beaten eggs.
Mix with hands for 1 full minute, or until eggs are evenly absorbed into meat.
Sprinkle anise seed, basil, garlic, salt, pepper, cornmeal and cheese over meat mixture and mix again with hands for 1 full minute, until all ingredients are evenly distributed.
Heat oil in a large skillet over medium heat. Scoop about 3 ounces of ham mixture into hands and form patties about 1/2 inch thick.
Lay patties in skillet and cook for 3 to 5 minutes each side, or until browned.
Drain on paper towels. Repeat until all of the mixture has been used, then serve hot.