To soak the glass noodles, in a bowl, add the glass noodles and pour in the hot water. Soak for about 5 minutes until softened, then drain and cut into about 2-inch lengths.
To cook the filling, in a pan over high heat, add the cooking oil, carrot, snow peas, shiitake mushrooms, and garlic. Stir-fry for about 2 minutes until aromatic and slightly softened. Add the glass noodles, vegetarian oyster sauce, and white pepper, then mix well. Let the filling cool for about 5 minutes.
To make the dipping sauce, in a bowl, mix together the soy sauce, Chinkiang vinegar, and chili oil.
To assemble the potstickers, in a bowl, whisk together the water and rice vinegar. Place a sheet of rice paper on a working surface and lightly brush both sides with the water mixture until softened but not overly wet. Place about 1 tablespoon of filling near the bottom corner, fold up the bottom, fold in the sides, and roll tightly. Repeat with the remaining filling and rice paper.
To pan-fry the potstickers, in a pan over medium heat, add the cooking oil and sprinkle in the salt. Transfer the potstickers to the pan and pan-fry for about 2 minutes per side until crispy and golden brown. Repeat with the remaining potstickers and serve with the dipping sauce.