In a large skillet, heat the olive oil and when the oil is hot add the mushrooms to the skillet. Season with salt and pepper. Sauté until the mushrooms release their liquid and it evaporates, and then the mushrooms begin to turn nicely browned. Transfer the mushrooms to a plate and cool to room temperature.
In a large bowl combine the egg, ponzu sauce, garlic and ginger. Finely chop the cooled mushrooms using a knife or by pulsing in the food processor, and then add them along with the beef to the bowl, and use to hands to gently mix until well combined.
Form the mixture into 6 patties, and use your thumbs to make slight indents in the center of each burger, which will cause them to end up flat when they cook. In a small bowl combine the mayonnaise with the wasabi paste, and taste to check if you like the level of heat – add more mayo or wasabi paste to adjust.
Preheat the grill to medium high. Grill the burgers for 4 to 5 minutes on each side, until they are done to your liking. Serve with the wasabi cream, or anything you like!