Bring broth and 1 cup water to a simmer in a medium saucepan (do not boil). Keep warm over low heat.
Heat oil in a large saucepan over medium-high heat. Add onion to pan; sauté 5 minutes or until tender. Stir in rice and garlic; sauté 1 minute. Add broth mixture, 1/2 cup at a time, stirring constantly until each portion of broth is absorbed before adding the next (about 30 minutes total).
Stir in asparagus and shrimp; cook 5 minutes or until shrimp are done, stirring constantly. Remove from heat; stir in cheese and remaining ingredients.