How to Make It
Heat a 10-inch ovenproof nonstick skillet over medium-low heat. Add 2 teaspoons olive oil to pan; swirl to coat. Add thinly sliced onion; cook 12 minutes or until onion is tender, stirring occasionally. Add chard; cook 10 minutes or until chard is tender, stirring occasionally. Sprinkle with 1/4 teaspoon salt and black pepper.
Combine parsley, 2 tablespoons basil, garlic, eggs, and remaining 1/4 teaspoon salt, stirring with a whisk. Add chard mixture to egg mixture. Stir in 1 ounce Gruyère cheese.
Preheat broiler to high.
Wipe pan clean with a paper towel. Return pan to medium-high heat. Add remaining 2 teaspoons oil to pan; swirl to coat. Add egg mixture to pan; cook 30 seconds. Reduce heat to low; cook, without stirring, for 4 minutes or until eggs are partially cooked. Sprinkle egg mixture with Parmesan cheese and remaining 5 ounce Gruyère cheese.
Place pan under broiler. Broil 1 minute or until eggs are thoroughly cooked and cheese is browned. Remove pan from oven. Run a silicone spatula around edge and under frittata to loosen from pan; slide frittata onto a plate or cutting board. Sprinkle with remaining 2 tablespoons basil. Cut frittata into 4 wedges.