Heat the broiler to high and arrange rack in upper third.
In a large bowl, whisk together eggs, cheese, salt, and freshly ground black pepper until thoroughly combined.
In a large ovenproof frying pan, heat the oil and the butter over medium-high heat. When it foams, add asparagus, season well with salt and freshly ground black pepper, and cook, stirring occasionally, until cooked through, about 5 minutes. Stir in the cilantro. Reduce heat to low, pour in egg mixture, and cook until a 1-inch border of egg mixture is firm, about 3 minutes. (The center of the frittata will not be set at this point.) Place the pan in oven and broil until some spots are browned and eggs are just set, about 2 minutes. Cut into wedges and serve with a side salad. It can be served warm or at room temperature.