In a large bowl combine the ham, onion, broccoli and beaten eggs. Mix with hands for 1 full minute, or until eggs are evenly absorbed into meat.
Sprinkle aniseed, basil, garlic, salt, pepper, polenta 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 frypan over medium heat. Form mix into 6 patties about 1 cm thick. Lay patties in frypan 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.