Melt the butter in a medium frying pan over medium-low heat, then cook the garlic and leeks until they are soft but not too brown, about 3 minutes. Pour in the heavy cream, and stir for another minute, until the leeks have absorbed some of the liquid. Remove from heat, transfer to a mixing bowl, and allow to cool. Add in all other ingredients except the flour, mixing thoroughly. Gradually work in the flour until you have a dense dough that isn’t too sticky.

Pour just enough oil into a frying pan to cover the bottom, and heat over medium-low. Using lightly oiled hands, form the rice mixture into patties roughly 5 inches across and 1/2-inch thick. Working in batches, drop the patties into the hot pan and cook for about three minutes, flipping halfway through, until golden on each side and cooked through.