Snap off thick ends of asparagus. Cut into 1/2-inch pieces. Blanch in salted water until bright green. Drain and refresh under cold water. Drain thoroughly. Preheat oven to 475 degrees F. Beat eggs with fork and season with salt and pepper. In large nonstick pan, heat oil and butter together over medium heat. Add the scallions. Stir and cook until wilted. Reduce heat to low and add asparagus. Cover skillet and cook 10 minutes until asparagus is tender. Season with salt and pepper.
Add peppers and chopped parsley to skillet and toss well. Spread evenly over bottom. Pour in egg mixture. Eggs should cover vegetables. Increase heat to medium. Cover and cook until crust forms underneath, about 2 to 3 minutes. Sprinkle with grated cheese. Transfer to oven and bake uncovered, until firm, 5 to 7 minutes. Remove from oven. Let stand for 5 minutes. Cut and serve.