Bring broth to a simmer in a medium saucepan (do not boil). Keep warm over low heat.
Heat oil in a large saucepan over medium heat. Add onion; sauté 5 minutes. Add garlic; sauté 1 minute. Add rice and next 3 ingredients; cook 1 minute, stirring constantly. Add wine; cook until liquid is nearly absorbed, stirring constantly. Add warm broth, 1/2 cup at a time, stirring constantly, until each portion of broth is absorbed before adding the next (about 25 minutes total). Stir in shrimp and spinach; cook 5 to 7 minutes or until shrimp turn pink. Stir in Parmesan cheese.