Preheat oven to 300°F (150°C). Place bread cubes on a rack set in a rimmed baking sheet and bake in oven until completely dried out, about 30 minutes.

If using store-bought chicken broth or homemade broth that remains watery when chilled, place stock in a large liquid measuring cup and sprinkle gelatin over the top. Set aside.

If Making Rice in a Pressure Cooker: Heat oil in pressure cooker over medium-high heat until shimmering. Add onion and cook, stirring occasionally, until onion is softened and translucent, about 4 minutes. Add rice and cook, stirring, until rice is evenly coated in oil and toasted but not browned, 3-4 minutes. Add wine and cook, stirring, until raw alcohol smell has cooked off and wine is almost fully evaporated, about 2 minutes. Stir in 3 cups broth and 1 pinch saffron, scrape any grains of rice or pieces of onion from side of pressure cooker so that they are fully submerged; season with salt. Close pressure cooker and bring up to low pressure (10 psi on most units). Cook at low pressure for 6 minutes, then depressurize cooker either by running it under cold water if it is not electric, or using the steam-release valve if it is electric. Return to heat and stir rice until it forms the texture of a thick porridge. Season with salt and pepper.

If Making Rice on Stovetop: Heat oil in large saucier pan or Dutch oven over medium-high heat until shimmering. Add onion and cook, stirring occasionally, until onion is softened and translucent, about 4 minutes. Add rice and cook, stirring, until rice is evenly coated in oil and toasted but not browned, 3-4 minutes. Add wine and cook, stirring, until raw alcohol smell has cooked off and wine is almost fully evaporated, about 2 minutes. Stir in 2 cups stock and 1 pinch saffron, scrape any grains of rice or pieces of onion from side of pressure cooker so that they are fully submerged; season with salt. When liquid has mostly evaporated, stir in 1 more cup stock and cook, stirring frequently, until liquid has mostly evaporated. Stir in water ¼ cup at a time until rice is just tender and has formed the texture of a thick porridge. Season with salt and pepper.

Meanwhile, in a small saucier or saucepan, melt butter over medium-high heat until foaming. Stir in 2 tablespoons flour to form a paste, lower heat to medium, and cook, stirring constantly, until raw-flour smell is gone but flour has not browned, 2 to 3 minutes. Whisk in milk and remaining ¾ cup stock until smooth, and add remaining 1 pinch saffron. Bring to a simmer, and continue to cook, stirring, until bechamel sauce is thick enough to coat the back of a spoon, about 4 minutes. Season with salt and pepper. Let cool slightly, then whisk in eggs.

Scrape rice into large mixing bowl along with bechamel sauce and stir until thoroughly incorporated. Line 2 rimmed baking sheets with parchment and scrape rice filling onto each one, spreading it in a thin, even layer. Refrigerate rice filling until thoroughly chilled and thickened, at least 1 hour.

Meanwhile, if making homemade bread crumbs, transfer dried bread cubes to a food processor and process until finely ground. Transfer homemade breadcrumbs or ground panko to a plate.

In a shallow bowl, whisk remaining ¼ cup flour with ¼ cup water to form a smooth paste, then whisk in an additional ¼ cup water to form a slurry.

Transfer chilled rice filling to a large mixing bowl and re-line rimmed sheets with fresh parchment paper. Scoop a small handful (about ¼ cup) of rice filling in one hand and form it into a flat disk. Place a few small pieces of mozzarella in center of disk and fold rice filling around it to form a sphere with the cheese in the center.

Roll rice ball in flour slurry, then transfer to breadcrumbs and roll to coat. The rice ball may feel a little soft at this point, but you should be able to coat it in the crumbs and just manage to maintain a roughly spherical shape. Transfer to parchment and repeat with remaining rice filling, cheese, and coatings.

Fill a saucepan at least 4 inches deep with vegetable oil and heat to 375°F (190°C). Pick up one breaded rice ball and re-form it into a sphere. Gently set it on a slotted spoon and lower it into the oil. Repeat with remaining rice balls, working in batches and topping up oil as needed. Fry rice balls until golden brown, then, using a slotted spoon or spider, lift them one by one from the oil, allowing excess oil to drip off, then transfer to paper towel-lined baking sheets or plates. Let cool slightly, then serve. Rice balls can be allowed to cool, then stored in the refrigerator. Reheat in a 350°F (180°C) oven.