Preheat oven to 450F. Spray a baking sheet with oil.
Put the beaten eggs in one bowl, and the breadcrumbs, panko and parmesan cheese in another.
Season shrimp with salt and pepper, then put a few at a time in the bowl with the eggs to coat.
Put a few pieces of shrimp at a time into the breadcrumb mixture to coat, then on a baking sheet.
Once all the shrimp is breaded, if you still have crumbs left, re-dip the shrimp back into the egg beaters and then back into crumbs and back onto the baking sheet.
Spray the top of the shrimp generously with oil then bake in the middle rack for about 6-7 minutes.
Turn shrimp over then cook another 3 minutes or until cooked though.
Remove from oven and serve right away with lemon wedges, if desired.