Preheat oven to 450°F (232°C).

Slice off the top of the garlic head.

Drizzle garlic with olive oil, season with salt and pepper, and wrap in foil.

Roast garlic in the oven for 45 minutes.

Trim green beans by removing the stems.

Bring a large pot of water to a boil.

Submerge green beans in boiling water for 2-3 minutes.

Transfer green beans to a bowl of ice water to stop cooking.

Let green beans cool in ice water for a few minutes.

Lay green beans on paper towels to dry.

Set up three shallow bowls: one for flour, one for beaten eggs, and one for panko bread crumbs, Parmesan cheese, onion powder, and cayenne pepper.

Season each bowl with salt and pepper.

Line a sheet pan with parchment paper.

Dredge green beans in flour, then in egg, and lastly in panko mixture.

Arrange green bean fries evenly on the sheet pan, avoiding crowding.

Remove roasted garlic from the oven, reduce oven temperature to 425°F (220°C).

Bake green bean fries at 425°F for 15 minutes.

While fries are baking, prepare the aioli.

Squeeze roasted garlic cloves into a bowl and mash with a fork.

In a separate bowl, combine mayonnaise, olive oil, Dijon mustard, salt, and pepper.

Add the roasted garlic paste to the mayonnaise mixture and combine.

Serve green bean fries immediately with roasted garlic aioli on the side.