Heat oven to 350°F. Cook rice in water as directed on package. Stir in butter. Cool 5 minutes.
Spray 8- or 9-inch cake or pie pan with olive oil nonstick cooking spray. Sprinkle pan with 1/4 cup of the bread crumbs. Set aside.
In medium bowl, beat egg and egg white until blended. Add cooked rice, cheese, green onions and 1 tablespoon of the parsley; mix well. Press into crumb-lined pan. Sprinkle remaining 1/4 cup bread crumbs evenly over top.
Bake 18 to 20 minutes or until center is set.
Meanwhile, heat oil in 10-inch nonstick skillet over medium heat until hot. Add onion; cook 4 minutes or until golden brown and caramelized, stirring occasionally. Add garlic; cook 1 minute, stirring constantly. Add all remaining ragout ingredients; mix well. Heat to boiling. Reduce heat to low; simmer uncovered 5 minutes.
To serve, cut rice cake into wedges. Place wedges on individual serving plates. Top each serving with ragout mixture. Sprinkle with remaining tablespoon parsley. If desired, garnish with shaved Asiago cheese.