Place green onions on a lightly greased rimmed baking sheet. Bake at 425° for 13 to 15 minutes. Chop onions, and set aside.
Heat oil in a saucepan over medium-high heat; add shallot and garlic, and sauté 30 seconds. Stir in wine; cook, stirring constantly, 4 minutes or until wine is almost evaporated.
Add rice. Cook, stirring constantly, 1 minute. Reduce heat to medium; add 1/2 cup broth. Cook, stirring constantly, until broth is absorbed. Repeat procedure with remaining broth, 1/2 cup at a time. (Total cooking time is about 22 minutes.)