In a large nonstick skillet, heat 2 tablespoons of the oil over moderate heat. Add the mushrooms and cook, stirring occasionally, until tender and beginning to brown. Add the cole slaw mix, scallions, garlic and ginger. Cook, stirring occasionally, until the vegetables are softened, 3 to 5 minutes. Add the chopped brisket and 2 tablespoons of the dumpling dipping sauce. Cook, stirring occasionally, until the brisket is heated through, about 2 minutes. Stir in the cilantro and season with salt, if needed. Scrape the filling into a medium bowl and wipe out the skillet.
Fill a heat-proof baking dish or skillet with 1 to 2 inches of very hot water and wet your cutting board (this is to prevent the rice paper wrappers from ripping). Line a large plate with damp paper towels.
Working one at a time, slide one rice paper into the hot water, gently rotating the wrapper with your hands for a few seconds to wet both sides. Place it on your work surface. Let it sit until completely pliable and slightly tacky, about 30 seconds. Spoon 3 tablespoons of the brisket filling into the center of the wrapper. Fold the top half of the wrapper over the filling, then fold the bottom half of the wrapper over the filling. Fold over the ends to create a snug packet. Moisten a second rice paper wrapper and transfer to your work surface. Place the wrapped dumpling in the center of your wrapper and repeat the wrapping process to create two rice paper layers. Transfer the dumpling to the prepared plate and repeat with the remaining wrappers and filling, adding more hot water as needed. You should have 10 large dumplings.
In the nonstick skillet, heat the remaining two tablespoons of the oil. Working in batches and adding more oil as needed, sear the dumplings over moderately-high heat, flipping once, until crispy and browned on both sides, 3 to 5 minutes.
Transfer the dumplings to a plate and garnish with sesame seeds, cilantro and scallions. Serve right away with the dipping sauce on the side.