In a shallow bowl, beat egg until all whites are no longer visible and it begins to form small bubbles. Pour flour into another bowl. In a third bowl, combine Panko breadcrumbs with ¾ teaspoon of kosher salt and freshly cracked pepper to taste.
In a medium saucepan or deep skillet, heat 1½ inches of vegetable oil to 350 degrees Fahrenheit. When the temperature approaches 325 degrees, begin breading the grouse: First lightly coat pieces in flour, and then in the egg, and then coat with the Panko mixture. Note: Watch the oil temperature carefully and get your ducks (or grouse) in a row before you add the meat; panko breadcrumbs can burn quickly. Use a candy/deep fryer thermometer and adjust the heat as necessary. Oil also shouldn’t be too cool; the breadcrumbs need to begin browning as soon as they hit the oil so that the grouse stays pink on the inside. The longer the meat needs to sit in the hot oil, the higher the chances that you’ll overcook the meat.
When oil reaches 350 degrees, fry breaded grouse until golden on both sides, flipping halfway through. Do not overcrowd the pan, and fry meat in batches if necessary. Drain and rest on a cooling rack or paper towels before serving. Serve grouse katsu with tonkatsu sauce, rice and chopped green onion.