In a medium bowl combine the leftover risotto, chicken egg, and Parmigiano-Reggiano (if needed). Season with salt and pepper.

Place a thin, even layer of panko or traditional bread crumbs — about 9-inches square — on a piece of parchment paper. Place a 4-inch ring mold in one of the four corners of the crumbs and spoon a fourth of the risotto mix into the mold. Tamp it down so that it will hold together, and even out the top. Sprinkle the top with breadcrumbs and press to make them adhere. Gently remove the ring mold, and move it to another corner, and repeat with another fourth of the risotto. Make two more risotto cakes in the same fashion.

Heat a skim of olive oil in a 10- or 12-inch nonstick skillet over medium-high heat. Using a broad spatula, gently place all four risotto cakes in the skillet and cook until golden brown on the bottom (you can see browning on the edges) — about 5-6 minutes. If a cake breaks, you can gently but firmly reshape it. If they come out looking more like randomly-shaped patties, don’t worry; they will still taste great! When the bottoms are browned, gently turn them over and cook 5-6 minutes longer until the other side is golden brown.

While the second side is cooking, melt some butter in the bottom of a 9-inch nonstick skillet over medium heat. Break the quail eggs into the pan (it is best to use quail egg scissors) and let them cook sunny side up, until the whites are fully cooked and the yolk is somewhat firm. (Unlike chicken eggs, little white spots will not appear to let you know the yolk is done.) Season with salt and freshly ground black pepper.

Plate each rice cake on a bed of lettuce (season with oil and vinegar, if you like), and top with a sunny side up quail egg.