Preheat oven to 425°F. Cover a baking sheet with parchment paper.
In a wide, shallow bowl combine panko, Parmesan cheese, ¼ cup flour, Italian seasoning, garlic salt, and pepper. Add remaining ½ cup flour to another wide bowl, and add eggs to a third bowl.
Dredge each asparagus spear in flour, then dip in eggs, then roll in panko mixture; press to coat. Place asparagus in a single row on the baking sheet with parchment paper. Bake for 10-12 minutes at 425°F, or until panko is golden brown and crispy.