Preheat oven to 350 degrees. Season short ribs on both sides with salt and pepper. Spread flour on a shallow plate. Dredge each short rib in flour to coat, shaking off excess.
Heat oil in a large Dutch oven over medium-high heat. Working in batches and reducing heat if necessary, sear short ribs on all sides, 3 to 4 minutes per side. Transfer to a plate.
Reduce heat to medium. Add vegetables to Dutch oven. Cook, stirring occasionally, until tender, 10 to 15 minutes. Return short ribs to Dutch oven. Add brandy, and cook for 2 minutes. Add stock, water, and halved kumquats. Bring to a boil. Cover, and transfer to oven. Bake until very tender, 2 1/2 to 3 hours. Transfer short ribs to a platter.
Pour sauce through a fine sieve into a small pot; discard solids. Skim off excess fat, and cook over medium heat until reduced by half, about 15 minutes. Serve short ribs with sauce, and whole kumquats if desired.