Make the aioli:
Preheat the oven to 400ºF.
Slice the top one-third off the head of garlic. Place the bottom portion on a piece of foil, drizzle it with olive oil, and season it with salt and pepper. Place the top portion back on the head of garlic and crumple the foil to create a sealed packet. Roast the garlic for 30 minutes or until it has softened.
Remove the roasted garlic from the oven and squeeze the cloves into a medium bowl. Add the mayonnaise and lemon juice, mashing with a fork until combined. Season the aioli with salt and pepper to taste. Cover with plastic wrap and store in the fridge until ready to serve.
Make the asparagus:
Reduce the oven to 375ºF. Line a baking sheet with parchment paper.
In a shallow baking dish, whisk together the egg whites with the mayonnaise. (The mayo helps the eggs adhere to the asparagus.)
In a separate shallow baking dish, combine the Panko breadcrumbs, chopped parsley and Parmesan cheese.
Dip each asparagus spear in the egg mixture until it's thoroughly coated then dredge it in the breadcrumbs, pressing to secure them to the asparagus.
Transfer the asparagus to the prepared baking sheet. Repeat the breading process with the remaining asparagus, spacing them about 1 inch apart on the baking sheet.
Lightly spray the asparagus with cooking spray and bake them for 15 to 20 minutes until golden brown and crispy.
Remove the asparagus fries from the oven and serve them immediately with the prepared roasted garlic aioli.