Sprinkle quail with salt and pepper. Place 1 (1-inch) rosemary sprig and 1 (1-inch) thyme sprig into cavity of each quail.
Heat oil in a large nonstick skillet over medium-high heat. Add quail; cook 3 minutes on each side or until browned. Arrange quail, breast sides up, in pan; add 1/2 cup broth. Partially cover, reduce heat to medium-low, and cook 25 minutes or until done. Place quail on a platter; cover loosely with foil.
Add 1/4 cup broth, prosciutto, grappa, and shallots to pan; cook over medium-high heat 1 1/2 minutes or until shallots are tender, scraping pan to loosen browned bits. Stir in 1/2 cup broth and whole and halved grapes; cook 2 minutes or until grapes are thoroughly heated. Pour grape mixture over quail; garnish with whole rosemary and thyme sprigs, if desired.