Preheat the oven to 375 degrees. Combine the rice, beets and herbs in a large bowl.
Purée the beans with the lemon juice and egg with a fork. Scrape into the bowl with the rice and beets. Add the goat cheese, salt and pepper, and mix the ingredients together.
Moisten your hands and form 6 patties.
Working in batches, heat 1 tablespoon of the oil at a time in a heavy ovenproof skillet and brown the patties on one side for 2 minutes. Turn over onto the other side and place in the oven for 10 minutes. Serve with or without buns, ketchup and the works.