Heat 1 tablespoon oil in a large high-sided skillet over medium-high heat until hot but not smoking. Season quail with salt and pepper and brown on all sides, about 7 minutes. Add half of the onion, and all of the carrot and celery; reduce heat to medium and cook, stirring, until vegetables are softened, about 5 minutes. Stir in tomato paste, parsley, sage and rosemary, then add 2½ cups broth, stir, and cook, covered, until quail is cooked through, about 30 minutes.

Transfer quail to a plate and loosely cover to keep warm. Add remaining 2½ cups broth to skillet and bring to a simmer; remove from heat.

Heat remaining 2 tablespoons oil in a heavy large saucepan over medium-low heat. Add remaining half of onion and cook, stirring occasionally, until onion is softened, about 7 minutes. Add rice and cook, stirring constantly, until rice is translucent, about 5 minutes.

Add wine and cook, stirring, until wine is mostly absorbed, about 4 minutes. Add 1 cup broth and cook, stirring, until liquid is mostly absorbed, 5 to 7 minutes. Add ½ cup more broth and cook, stirring, until mostly absorbed. Repeat, adding liquid in ½ cupfuls, until rice is tender yet still slightly firm to the bite, and risotto is all’onda (a bit liquid, broth not fully absorbed). Stir in cheese and butter.

Season risotto with salt to taste, divide among bowls, top with quail and serve immediately.