Lightly salt and pepper eggplant slices. Heat 1/8-inch oil in heavy 10-inch skillet over high heat. Add eggplant (in batches; do not crowd) and brown well on both sides. Remove using slotted spatula and drain on paper towels. Pat eggplant dry. Line six 4 ounce ramekins with eggplant, using about 3 slices each; do not trim overhang.
Bring broth to a boil. Reduce heat to gentle simmer. Heat 2 tablespoons oil in heavy 4-quart sauce pot over medium heat. Add onion and cook until translucent, stirring occasionally, about 7 minutes.
Add rice and stir until opaque, about 2 minutes. Mix in saffron. Add simmering broth and cover. Lower heat to low and cook 45 minutes to 1 hour or until rice is tender.
Remove from heat. Stir in cheese and asparagus. Season with salt and pepper Spoon rice mixture into prepared ramekins, pressing firmly. Fold eggplant over rice to enclose completely.
Line Platter with spinach leaves. Run knife around ramekins. Unmold onto platter. Can be reheated in microwave.
Cajun Country -- New Iberia, Louisiana