To make the rice, melt the butter in a medium pot over medium heat. Add the rice to the pot and cook 2-3 minutes, until just slightly toasted. Add 1/2 cup of the chicken broth and cook, stirring frequently, until the liquid is cooked off. Add the remaining chicken broth, 1 cup at a time, stirring frequently and allowing the rice to thicken between additions. Cook 20-25 minutes, until the rice is tender and thick. Remove from heat and stir in the salt, pepper, eggs, and parmesan. Move the rice to a bowl, cover, and refrigerate until chilled completely, at least two hours.
To make the filling, add the ground beef and ground pork to a large skillet over medium heat. Cook, breaking into small pieces, until browned and cooked through. Drain the grease and return the meat to the skillet. Add the tomato paste, tomato sauce, garlic salt, basil, oregano, sugar, and water. Bring the filling to a simmer and cook until thickened, about 10 minutes. Remove from heat and stir in the peas, then allow to cool slightly.
Add the bread crumbs to a shallow dish. In another shallow dish, beat together the eggs. Heat the vegetable oil to 360 degrees in a deep skillet or shallow pot.
To assemble the rice balls, scoop two tablespoons of the rice mixture into the palm of your hand and flatten slightly to form a cup. Add a teaspoon of the filling mixture to the center of the cup, then fold the rice around the filling to form a ball. Dip each ball in the egg mixture, then roll in the bread crumbs. Place the balls on a cookie sheet until they are all assembled.
When the oil has heated, place the rice balls, 3-4 at a time, into the hot oil. Cook 3-4 minutes per side, until golden brown and crispy on all sides. Drain on paper towels. Serve warm, sprinkled with parmesan cheese, with marinara sauce for dipping.