Preheat oven to 400°. Whisk first 7 ingredients in a medium bowl; set aside. Heat oil in a medium ovenproof nonstick skillet over medium-high heat. Add onion; sauté until soft, about 6 minutes. Reduce heat to low. Stir in egg mixture. Spoon diced cheese evenly over.
Cook until frittata begins to set, about 2 minutes. Place in oven; bake until just set, 7-9 minutes. Slide the frittata onto a platter. Cut into wedges; serve hot or at room temperature.