How to Make It
Preheat oven to 350°.
Combine first 3 ingredients; add 1/4 teaspoon salt, stirring with a whisk. Heat a 10-inch ovenproof skillet over medium-high heat. Add 2 teaspoons oil; swirl to coat. Add mushrooms and remaining 1/4 teaspoon salt; sauté 6 minutes or until mushrooms brown and most of liquid evaporates. Stir in onions; sauté 2 minutes. Reduce heat to medium. Add egg mixture and basil to pan, stirring gently to evenly distribute vegetable mixture; cook 5 minutes or until eggs are partially set. Place pan in oven. Bake at 350° for 7 minutes or until eggs are cooked through and top is lightly browned. Remove pan from oven; let stand 5 minutes. Run a spatula around edge and under frittata to loosen from pan; slide frittata onto a plate or cutting board.
Combine the remaining 1 teaspoon oil, arugula, and lemon juice. Cut the frittata into 6 wedges; top with arugula mixture.