Heat 1 tablespoon vegetable oil in a large skillet over medium-high heat.

Add the mushrooms, cabbage, and carrots and stir-fry for 3-4 minutes until slightly softened.

Add the scallions and garlic and cook for another minute. Stir in the soy sauce and sesame oil, then remove from the heat and allow the filling to cool.

Dip one rice paper wrapper briefly in warm water until it begins to soften, then place it on a clean work surface.

Place about 2 tablespoons of vegetable filling near the lower center of the wrapper. Fold in the sides and roll tightly. Repeat with the remaining wrappers and filling.

Let the finished rolls rest for several minutes so the surface becomes slightly tacky and less wet before frying.

Heat a thin layer of vegetable oil in a large skillet over medium heat. Fry the spring rolls in batches, leaving space between them.

Cook for 2-3 minutes per side, turning carefully, until crisp and golden. Transfer to a wire rack or paper towel-lined plate.

To make the sauce, combine the rice vinegar, brown sugar, ketchup, soy sauce, and 1/2 cup water in a saucepan. Bring to a gentle simmer. Stir together the cornstarch and 2 tablespoons water, then whisk it into the sauce and cook until thickened.

Serve the crispy spring rolls warm with the sweet and sour sauce on the side.