Prepare the cilantro lime aioli. Combine all of the ingredients in a blender and blend until smooth. Set aside.
Pour enough frying oil into a deep saute pan until it's about ½ inch high. Preheat to 350 degrees F.
Slice mushroom caps into 1 inch thick slices. Set aside.
Combine flour with seasonings from garlic salt - black pepper in a medium bowl. Whisk eggs in a separate bowl. Put parmesan in a third bowl.
Dredge the sliced mushrooms in flour. Dip them in the egg then coat with shredded parmesan. Carefully drop the mushrooms into the hot oil and fry until golden brown, about 3-4 minutes, flipping halfway through. Remove from oil and drain on paper towels. Serve with cilantro lime aioli.