Saute the shallot and garlic with the butter in a saute pan over medium heat. Add the ham, cook until lightly crisp and then stir in the rice.
Mix the ham mixture, cream cheese, Parmesan, mozzarella, and parsley together in a large mixing bowl. Season with salt and pepper, to taste. Roll the mixture into 2-inch balls and put on a baking sheet.
Add the flour, beaten eggs, and panko to separate pie plates. Season the panko with salt and pepper. Roll the balls through the flour, then the egg and then the panko. Gently add the fritters to the deep-fryer and fry until golden and crisp, 3 to 4 minutes. Transfer the fritters to a serving platter and serve.