Preheat oven to 400 degrees F. Line a baking sheet with foil. Coat foil with cooking spray; set baking sheet aside.
If using Swiss chard, separate stems from leaves. Cut stems and leaves into bite-size pieces, keeping them separate.
In a large nonstick skillet heat 2 teaspoons of the oil over medium-high heat. Add 2/3 cup of the red onion, the garlic, and salt; cook for 2 minutes. If using chard, add stems and cook for 5 minutes, stirring frequently. Add chard leaves or spinach; cook about 5 minutes or until chard is wilted and moisture is nearly evaporated, stirring occasionally. Add asparagus; cook and stir about 3 minutes more or until asparagus is crisp-tender. Spread mixture on a plate to cool slightly.
For crust, in a medium bowl combine eggs, egg white, oregano, the 1/4 teaspoon pepper, and the nutmeg. Stir in cooked rice, Parmesan cheese, and Swiss chard mixture. Spoon mixture onto the prepared baking sheet. Using your hands, press into a 12-inch circle. Bake for 10 minutes. Remove from oven.
Preheat broiler. Broil crust 4 to 5 inches from the heat for 1 to 2 minutes or just until golden. Sprinkle with Havarti cheese. Broil for 1 minute more. Remove from broiler. Let stand for 2 minutes. Lift one corner of the foil and carefully slide a cutting board underneath crust; let stand for 1 minute more.
In a medium bowl combine the remaining 1 teaspoon oil, the remaining red onion, grape tomatoes, yellow sweet pepper, pepperoncini peppers, parsley, vinegar, and the 1/8 teaspoon pepper. To serve, cut crust into wedges. Top with tomato mixture.