Pour oil to a depth of 1 1/2 inches in a medium skillet. Heat oil to 375 degrees.
Slice avocado into 1/2 inch thick wedges.
Pour the flour and 1/2 teaspoon salt into a shallow dish. and stir to combine. Add the eggs to another shallow dish, and the panko and remaining 1/2 teaspoon salt to a third dish.
Dredge the avocado wedges in the flour, then the eggs, and finally the panko.
Fry in batches for 1 minute or until golden brown, turning over halfway through.
Drain on a paper towel lined plate. Place on a baking sheet in a 200 degree oven to keep warm while frying the rest of the avocados. Season with more salt to taste.
When choosing avocados to fry, you'll want to pick avocados that are still fairly firm but not completely unripe. Perfectly ripe avocados will be too soft to handle easily and they'll soften even more as they cook.