To make the walnut sauce, blend the walnuts in a food processor until finely ground. Add the 1 tablespoon olive oil, 1 ½ tablespoons soy sauce, lime juice, honey, and Sriracha and continue to blend until a paste forms. Add the hot water and blend until a smooth sauce forms. Add more water as needed if sauce is too thick. Set sauce aside.
Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the ginger and garlic; cook and stir 1 minute until fragrant. Add the mushrooms, cabbage, and carrots and cook a few minutes until softened. Stir in the walnuts. Remove the skillet from the heat. Stir in the scallions, soy sauce, sherry and sesame oil.
Place a heaping teaspoon of the filling mixture in the center of each wonton wrapper. Dip your finger in a bowl of water and wet the edges of the wrapper. Fold in half and pinch together, pleating the dough as you seal it. Repeat with the remaining wrappers.
Heat 1 tablespoon olive oil in a nonstick skillet over medium high heat. When the oil is hot, add a batch of the dumplings to the pan. Cook a few minutes until brown on the bottom. Pour ¼ cup water into the pan and cover it with a lid. Steam 2-3 minutes. Uncover the pan and cook another minute or two until the water is completely evaporated. Remove potstickers from the pan. Cover to keep warm. Repeat with remaining potstickers. Serve potstickers with the walnut sauce for dipping. Garnish with walnuts and scallions.