In a shallow dish combine crumbs and half the cheese. In another shallow dish, beat together egg and water. Cut meat in 8 equal-size portions; lightly sprinkle with salt and pepper. Dip in egg mixture, then crumb mixture; press lightly to coat.
In a 12-inch skillet heat 1 tablespoon olive oil over medium-high heat. Working in two batches, cook steak, about 5 minutes per side, adding more oil as needed. Remove to a serving platter; cover to keep warm. Carefully wipe skillet clean.
Meanwhile, for sauce, in blender or processor combine drained peppers and remaining cheese. Process until nearly smooth. Finely chop 1/2 cup of the basil; set aside. Transfer pepper mixture to hot skillet and heat through. Remove from heat. Stir in finely chopped basil. Pour sauce over steaks. Sprinkle with remaining basil.