Bring the chicken broth to a boil in a medium saucepan (2+ quarts). Add the rice and cook for 15 minutes, stirring occasionally. *This cooking method ensures all the liquid is absorbed and the starch remains in the pan. This gives a dry, compact rice that can be used the same day.
Once all the liquid has been absorbed, remove the pot from the heat. Add the butter and parmesan and stir until thoroughly mixed. Spread the rice evenly over a baking sheet or platter and cover with plastic wrap. Chill in the fridge for 1 hour.
Fill a small bowl with water and set it to the side so you can moisten your hands as needed. Take a few spoonfuls of cooled rice and press them together in the palm of your hand. Use your thumb to make an indentation and fill it with 2 pieces of mozzarella. Form the rice into a ball that completely encases the cheese. Repeat with the remaining rice and cheese.
Set up a dredge station using two bowls. To the first bowl, add the flour, salt, and water. Whisk together to make a batter. To the second bowl, add the breadcrumbs.
Dip each rice ball first into the batter, letting any excess drip back into the bowl. Then roll it around in the breadcrumbs until completely coated.
Heat the oil in a large pot until it reaches 320-340 degrees F. Fry 3-4 arancini at a time until golden brown. Transfer the cooked balls to a paper towel-lined plate to drain. Repeat with the remaining arancini.*The balls will sink to the bottom of the pot. Be sure to turn them as they cook to prevent burning. You don't want the oil to get too hot, or the outside will overcook, and the cheese inside won't melt.
Garnish with chopped parsley is desired. Serve warm with a bowl of marinara sauce for dipping.