Bring broth and 2 cups water to a simmer in a medium saucepan (do not boil). Keep warm over low heat.
Heat 2 teaspoons oil in a large saucepan over medium-high heat. Add minced onion, celery, and carrot; sauté 1 minute. Add rice; sauté 5 minutes. Stir in wine; cook 5 minutes or until liquid is nearly absorbed, stirring constantly. Add broth mixture, 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 Parmesan cheese and green onions.
Preheat oven to 375°.
Remove stems from mushroom caps; discard. Place mushroom caps, gill sides up, in a 13 x 9-inch baking dish. Spoon 1 1/4 cups risotto mixture into each cap; top each with 1 tablespoon mozzarella cheese. Pour 1/2 cup water into dish. Bake at 375° for 30 minutes or until mushroom caps are tender.
Heat 1 teaspoon oil in a large Dutch oven over medium-high heat until hot. Add chopped onion and garlic; sauté 2 minutes or until tender. Add spinach; sauté 2 minutes or until spinach is wilted. Arrange 1/2 cup spinach mixture on each plate. Remove stuffed mushrooms from baking dish with a slotted spoon; place on spinach mixture.