Trim and discard root end of fennel bulb. Trim stalks from bulb, reserving fronds for another use. Cut bulb into fourths, and thinly slice. Set aside.
Sauté shallots in 1 tablespoon hot oil 3 minutes or until tender; stir in garlic and rice. Stir in wine and 2 1/2 cups water; bring to a boil. Cover, reduce heat, and simmer 35 minutes. Remove from heat; cover and let stand 15 minutes or until all liquid is absorbed.
Sauté fennel in remaining 1/2 tablespoon hot oil 1 minute. Add remaining 1/2 cup water, balsamic vinegar, salt, and pepper; simmer 8 minutes or until fennel is tender and liquid has evaporated. Stir into rice mixture.