In a Dutch oven or a heavy-bottomed pot with a tight-fitting lid over medium-high heat, add the olive oil and the butter and heat until the butter is melted.
Add the onions to the oil mixture and cook, while stirring, until softened and golden, about 4-5 minutes.
Add the ham to the onions and cook, while stirring, until golden, about 2 minutes.
Add the rice to the onion mixture and stir to combine.
Add the white wine to the rice mixture and cook, while stirring, until it is mostly evaporated, about 2 minutes.
Add the hot chicken broth and 1 teaspoon of the salt to the rice mixture and stir to combine.
Cover the pot and let it simmer until the rice has absorbed almost all of the liquid but isn't quite finished cooking, about 15-17 minutes.
Add the peas to the rice mixture and stir to combine.
Cover the pot with the lid and cook until the liquid is completely absorbed and the rice is tender, about 2 minutes.
In a large, rimmed baking dish, add the rice mixture and spread it out to cool to room temperature.
Add 1/3 cup of the parsley and 1 cup of the parmesan to the rice mixture and stir to combine.
Using damp, clean hands, form the rice mixture into 24 balls.
Stuff each of the rice balls with 1 cube of the mozzarella cheese, forming the rice mixture tightly around it. Make sure the rice completely covers the cheese cubes.
In a shallow bowl, add the flour.
In a separate shallow bowl, add the beaten eggs.
In a separate shallow bowl, add the Italian breadcrumbs.
Dredge each of the stuffed rice balls in the flour, shaking off any excess.
Dip each of the flour-coated rice balls in the beaten eggs, allowing the excess egg to drip back into the bowl.
Dip each of the egg-coated rice balls in the breadcrumbs, making sure they are evenly coated.
In a deep pot over medium heat, add about 1-inch of the neutral-flavored oil and heat it about 350 degrees F.
In batches, add the breaded rice balls to the hot oil and cook, turning them as needed, until all sides are golden-brown, about 3 minutes.
Transfer the cooked rice balls to paper towels to drain and sprinkle them with the extra salt.
Repeat until all of the rice balls are cooked, adding more of the neutral-flavored oil as needed and making sure the oil is back up to 350 degrees F before each batch.
Serve the rice balls with the extra parsley, the extra parmesan, and the marinara sauce.