Combine broth and water in a sauce- pan (do not boil). Keep warm over low heat.
Heat oil in a medium saucepan over medium-high heat. Add onion; sauté 2 minutes. Add rice; reduce heat to medium and cook 3 minutes, stirring constantly. Stir in wine; cook until the liquid is nearly absorbed, stirring constantly. Add broth mixture, 1/2 cup at a time, stirring constantly; cook until each portion of broth is absorbed before adding the next (about 20 minutes). Stir in crabmeat, parsley, and basil; cook 2 minutes or until thoroughly heated, stirring constantly. Spoon onto plates; sprinkle with cheese.