Preheat the oven to 400°F (200°C).
In a large pot, heat the olive oil over medium heat. Add the whole garlic cloves and cook for about 30 seconds, just until fragrant.
Remove and discard the garlic if desired.
Add the Arborio rice and stir for 1 to 2 minutes, allowing each grain to toast lightly and become coated in the oil.
Pour in the passata, water, and salt. Stir well to combine and bring to a gentle simmer.
Cook for about 20 minutes, stirring occasionally, until most of the liquid has been absorbed and the rice is almost tender. It should still have a slight bite, as it will continue cooking in the oven.
Remove from the heat and let the rice cool for 15 to 20 minutes.
Once cooled slightly, stir in the beaten eggs and grated Pecorino Romano until evenly combined.
Spread half of the rice mixture into a lightly greased 9 x 13-inch baking dish.
Arrange the prosciutto cotto in an even layer over the rice, followed by the scamorza or mozzarella.
Top with the remaining rice, spreading it evenly to completely cover the filling. Sprinkle generously with additional Pecorino Romano.
Bake for 20 minutes, or until the rice is set and the top is lightly golden.
For an extra crispy top, switch the oven to broil for the final 3 to 5 minutes, watching carefully to prevent burning.
Let the baked rice rest for 15 to 20 minutes before slicing and serving.