Make sauce. In a small bowl, mix together mayonnaise, soy sauce and wasabi paste.
In a medium-large bowl, mix together all-purpose flour, cornstarch and water. (not mix too much)
Put shrimp, edamame and onions into the flour mixture bowl. Mix to combine.
In a large work or fry pan, heat enough canola oil to deep-fry kakiage tempura. Divide the shrimp mixture into four, scoop with slotted spoon and drop into the oil one by one. Deep-fry over medium heat until lightly brown and crisp. (about 5 minutes) Turn and deep-fry the other side until lightly brown and crisp. (about 4 minutes) Drain on paper towels.
Spread the sauce on the bottom of each roll, put 1 kakiage tempura and 1 slice swiss cheese on top. Assemble 3 more sandwiches. Then place sandwiches on a baking sheet with the top of the rolls. Broil in the oven until cheese melt.
Take the baking pan out of the oven, put the top of each roll to close each sandwich. Serve immediately,