To make the shrimp filling: In a mixing bowl, combine the shrimp, shiitake mushrooms, scallions, ginger, salt, white pepper, and sesame oil. Mix until well combined.
To make the water mixture: In a small bowl, stir together the room-temperature water and rice vinegar.
To assemble the dumplings: Place a sheet of rice paper on your work surface. Brush both sides with the water mixture until just softened. Add about 1 tablespoon of the shrimp filling to the bottom corner of the rice paper. Fold up the bottom, fold in both sides, and roll tightly to seal. Repeat with the remaining dumplings. Lightly sprinkle each dumpling with cornstarch.
To pan fry the dumplings: In a pan over high heat, add the cooking oil and a pinch of salt. Arrange the dumplings in a single layer and fry for about 2 minutes per side, or until golden brown and crispy. Transfer to a wire rack or paper towel-lined plate. Repeat with the remaining dumplings.
To make the dipping sauce and serve: In a small bowl, whisk together the soy sauce, Chinkiang vinegar, and chili oil. Serve the crispy shrimp dumplings hot with the dipping sauce.