In a small bowl, mix the mayonnaise, Dijon, black pepper and garlic powder.
Spread the mayonnaise mixture on one side of each slice of bread.
Place the bread, mayonnaise mixture side down, in the cornflake crumbs. Press lightly. Set aside.
In a small skillet, heat the oil and butter. Saute the asparagus until crisp-tender and season with salt and pepper. Remove the asparagus to a plate, and keep warm.
In the same skillet fry an egg (seasoned with salt and pepper) until your desired doneness. Remove the egg to a plate, and keep warm.
Place one slice of bread in the skillet (cornflake side down), add two slices of provolone cheese, the egg, the sauteed asparagus, two more slices of the cheese, and the last slice of bread, mayonnaise side out.
Cook until browned, flip, and cook again until the cheese is fully melted.