In a large 1-gallon pot, heat 2 inches of peanut oil to 350 degrees F. Fry the wontons in batches until golden and crispy, about 90 seconds. Remove from the oil and drain on a paper-lined plate. Season with salt and reserve until ready to assemble the lasagnas.
Place a 12-inch saute pan over medium-high heat and add the oils. Once the oils are hot, add the garlic, ginger, and green onions, and stir with a rubber spatula for 30 seconds, to keep from burning. Add the carrots and peppers to the pan and saute, while stirring for 2 minutes. Add the cabbage to the pan and continue to cook for 3 minutes. Pour the water into the pan and continue to cook until all of the water is dissolved, about 3 minutes longer. Season the cabbage with the hoisin, salt, and pepper. Garnish with the green onions and cilantro and toss to blend.
Place 1 wonton skin on the base of 4 separate plates. Divide the vegetables among the 4 plates, and top each with another wonton skin. Continue by adding the meat mixture onto the second wonton.
Place a 10-inch saute pan over a medium-high heat and add the oils. When the oil is hot, add the garlic, ginger, and green onions to the pan. Saute for 30 seconds, and add the pork. Cook the pork, stirring occasionally, until most of the fat has rendered out and there is very little pink to be seen, about 3 minutes. Add the diced shrimp to the pan and continue to cook, stirring, for another 2 minutes. Add the hoisin, soy sauce, and 1 tablespoon sugar to the pan, and cook, stirring, until the liquid is reduced slightly, about 1 minute. Add the cornstarch slurry to the pan and cook, stirring for 1 minute longer. Sprinkle the fresh cilantro over the pan and toss to blend.
Layer the second wonton skin with the meat mixture and top with the third and final wonton skin. In the same pan that you cooked the pork and shrimp in, add the remainder of the soy sauce (1/4 cup), remaining 1 tablespoon of sugar, the mirin, and the shrimp halves. Place this over a high heat, and cook, until the shrimp are cooked and the liquid has reduced to a glaze, about 3 minutes.
Place a shrimp half on top of each wonton, and garnish with the cilantro. Drizzle the glaze around the lasagna on the plate and serve immediately.
Yield: 4 appetizer portions