Bring broth and water to a simmer in a medium saucepan (do not boil). Keep warm over low heat.
Heat oil in a large nonstick skillet coated with cooking spray over medium-high heat. Add mushrooms and onion; sauté 4 minutes. Remove from heat; set aside and keep warm.
Place rice in a Dutch oven over medium-high heat; cook 1 minute. Stir in vermouth; cook, stirring constantly, 1 minute or until liquid is nearly absorbed. Reduce heat to medium-low; add broth, 1/2 cup at a time, stirring constantly, until each portion of broth is absorbed before adding the next (about 20 minutes total). Remove from heat; stir in reserved mushroom mixture, spinach, and remaining ingredients. Serve immediately.