Arrange oven racks to that they are in the center and second-lowest positions. Preheat oven to 425°F. Line a 13- by 18-inch sheet pan with aluminum foil and top with a wire rack.
Place flour in a shallow dish. Season with ½ teaspoon garlic salt and a generous amount of black pepper; whisk to combine. In a second shallow dish, beat eggs and season with remaining ½ teaspoon garlic salt and more black pepper. Mix together panko and Parmesan in a third shallow dish.
Wash asparagus and trim off the tough ends. Working with a few pieces at a time, dredge in flour, then coat with eggs, and roll in panko/Parmesan mixture. Arrange asparagus on wire rack-topped baking sheet so that there's a little bit of space between each piece.
Place baking sheet on the middle rack in the oven and bake for 7 minutes. Move baking sheet to the 2nd lowest rack and bake for 3 to 5 minutes more, or until asparagus are crispy and golden. Serve immediately