Preheat oven to 400°. Whisk eggs and egg whites in a medium bowl until frothy; mix in basil and season with salt and pepper.
Heat oil in a medium ovenproof nonstick skillet over medium-high heat. Add asparagus and cook, tossing occasionally, until beginning to soften, about 2 minutes. Reduce heat to medium and add egg mixture, stirring to combine
Cook, shaking pan occasionally, until egg mixture is set around edges, about 4 minutes. Transfer skillet to oven and cook frittata until top is puffed and completely set, 10–15 minutes.
Run a heatproof spatula around edge of pan to release frittata. Slide frittata onto a warmed plate and cut into wedges.
