Heat 2 tablespoons oil in medium skillet over medium-high heat. Add artichokes to skillet; sprinkle with salt and pepper and sauté until beginning to brown around edges, about 4 minutes.
Add garlic and sauté an additional 2 minutes. Remove from heat.
Whisk eggs and 3 tablespoons cheese in large bowl. Sprinkle with salt and pepper.
Heat 2 tablespoons oil in medium nonstick ovenproof skillet over medium-high heat. Add mushrooms; sauté until browned, about 5 minutes. Add artichokes to skillet and stir 2 minutes. Add eggs; stir to blend. Reduce heat to medium, cover, and cook until eggs are almost set, about 5 minutes.
Sprinkle with remaining cheese.
Transfer frittata to broiler. Broil just until set in center and the top is golden brown, about 3 minutes. Using rubber spatula, loosen edges of frittata and slide out onto platter. Serve warm with a dollop of sour cream or plain yogurt on a plate garnished with the chopped scallions.