Preheat oven to 400°.
Heat oil in a Dutch oven over medium heat. Add onion; cook 4 minutes or until tender. Add rice; stir well. Stir in spinach, broth, salt, and nutmeg. Bring to a simmer; cook 7 minutes. Stir in 1/4 cup cheese.
Cover and bake at 400° for 15 minutes. Stir in asparagus; sprinkle with 1/4 cup cheese. Cover and bake an additional 15 minutes or until liquid is almost absorbed.