Mix the cornstarch, soy sauce, and 1/3 cup water in a small bowl. Set aside.
Heat the oil in a wok or a wide skillet. When a haze appears, add the mushrooms, scallions, ginger, and carrot and stir fry for about 3 minutes. Add the cabbage, sprinkle with 1 teaspoons salt, and stir fry until bright green and starting to turn limp, about 2 minutes.
Stir in cornstarch mixture and stir fry until the veggies are coated and the pan is dry, 1-3 minutes. Turn off the heat. Taste for salt and move the vegetables to a bowl to cool.
Form the spring rolls by laying the egg roll wrapper on the counter at a diagonal, with a corner facing you. Heap 2 tbls. of the filling crosswise, near the base. Cover it with sprouts before rolling. Fold up the lower corner, fold in the outer corners, then wrap. Repeat, using the rest of the filling. Place the egg rolls on a plate and cover with wax paper, then with plastic, until ready to cook.
To cook, heat 1/2" peanut oil in a medium skillet until hot enough to quickly sizzle a corner of an egg roll. Add two egg rolls and fry until golden, about 2 minutes. Turn and fry the second side, then remove to paper toweling to drain. Continue frying the rest. Serve hot with or without dipping sauce. Enjoy!