Bring broth to a simmer in a medium saucepan (do not boil). Keep warm over low heat.
Cook asparagus in boiling water for 3 minutes or until crisp-tender. Drain and rinse with cold water; drain.
Heat oil in a large nonstick skillet over medium-high heat. Add onion; sauté 5 minutes or until tender, stirring frequently. Add rice; cook 3 minutes, stirring constantly. Stir in 1 cup broth; cook 5 minutes or until the liquid is nearly absorbed, stirring frequently. Stir in 1/2 cup broth, vermouth and salt. Add remaining broth, 1/2 cup at a time, stirring frequently until each portion of broth is absorbed before adding the next (about 25 minutes). Add asparagus and shrimp; cook 4 minutes. Stir in cheese and remaining ingredients.