Bring broth to a boil in a large pot. Stir in both types of rice, cover and cook over medium low heat until rice is tender, about 35 minutes. Drain any excess liquid, rinse under cold water, and drain again.
Preheat oven to 425 degrees F and spray a baking sheet with nonstick cooking spray.
In a bowl, mix together cooled rice and the next 8 ingredients, mix very well. Measure out 1/4 cup of mixture and form into 10 patties; place on baking sheet.
Bake until browned, about 10 minutes per side.
While baking, heat tomato sauce, milk, and basil in a small pot; serve with rice cakes.