In a large bowl mix first 8 ingredients and 1 cup of panko. Use your hands and mix just to combine, trying not to break all of the lumps. Set aside.
Mix remaining 1/4 cup panko and parmesan cheese in a separate bowl. Use a quarter cup measuring cup to scoop up the crab mixture and form each portion into 2″ cakes. Dip each cake into the panko and parmesan mixture to coat. Place dipped cakes on a parchment paper-lined cookie sheet. Cover with plastic wrap and refrigerate for 30 minutes or more.
Make sauce by combining lime juice, soy sauce, Thai fish sauce, rice wine vinegar, brown sugar and chopped green onion. Set aside until ready to serve.
Heat a large frying pan and add 1 T olive oil and 1 T canola oil. When oil is hot add 6 crab cakes and cook until well browned on each side, about 2 minutes per side. Remove and place on paper towel-lined plate. Add remaining oil to pan, allow oil to get hot and then cook remaining 6 crab cakes. Serve immediately.