Boil the rice in salted boiling water, cook it and, after draining, place it in a salad bowl. Meanwhile, cook the peas in a pan with a little bit of oil. Pour the peas into the salad bowl with the rice, add the cooked ham, egg, grated cheese and mix everything together. Scoop out some of the mixture with a tablespoon and form small balls, helping yourself with your hands. Roll them in breadcrumbs and then fry them in hot oil; serve the patties piping hot.
If you want a lighter dish, you can bake the patties in the oven at 180° for 20 minutes and then for a few more minutes under the grill to brown them.