In a medium pot, heat 2 tablespoons olive oil over medium heat. Add the chopped ¼ yellow onion and sauté until soft and translucent.
Add the 2 cups Arborio rice and stir for 1–2 minutes to lightly toast. Season with ½ tsp salt and ¼ tsp black pepper.
Pour in the 1 cup ragù and 1 cup chicken stock (or water), stirring briefly to combine. Bring to a boil, then cover and reduce to a simmer. Cook for about 15 minutes, or until the liquid is absorbed and the rice is tender. Do not stir while it cooks.
Remove the rice from the heat and stir in ½ cup grated Pecorino Romano (or Parmesan) while still hot.
Spread the rice thinly onto a baking sheet to stop the cooking process and allow it to cool for about 15 minutes at room temperature. Then transfer to the refrigerator and chill until completely cold.
Place the cold rice in a large bowl and mix in the 3 eggs until fully combined.
With damp hands, take about 2 tablespoons of rice and flatten it slightly in your palm. Add a piece of 1 strip of mozzarella in the center, then cover with 2 more tablespoons of rice and shape into an oblong oval (the shape should resemble a pill but should be much larger), making sure the cheese is fully enclosed. Repeat with remaining rice.
Arrange the shaped supplì on a tray and refrigerate for at least 30 minutes, or until firm.
Prepare a coating by whisking the 3 eggs in one shallow bowl. Place the 2 cups seasoned breadcrumbs in a separate shallow bowl.
Dip each supplì into the eggs, then roll in the breadcrumbs until evenly coated. For a thicker crust, repeat the coating and breadcrumb step a second time. Return to the refrigerator for another 30–60 minutes.
Heat vegetable oil in a deep pot to 350°F. Fry the supplì in batches for 3–5 minutes, turning as needed, until golden brown and crisp on all sides. The centers should be heated through (about 150 degrees Fahrenheit) and the cheese melted.
Remove with a slotted spoon and drain on a paper towel-lined plate. Serve warm.