For the dipping sauce - put all ingredients in food processor and blend. Pour in a container and refrigerate until ready to serve.
In a medium saucepan, heat 1 1/2 in. oil until it registers 375° on a deep-fry thermometer.
Meanwhile, mix flour with 1/4 tsp. salt in a shallow plate. Put eggs and panko in separate shallow plates. Dip avocado in flour, shaking off excess. Dip in egg, then panko to coat. Set on 2 plates in a single layer.
Fry 2 to 3 avocado slices at a time until deep golden, 30 to 60 seconds. Transfer slices to a plate lined with paper towels. Keep warm in oven while cooking remaining avocados. Sprinkle with salt to taste.