In a large pan, sauté mushrooms until brown in 1 teaspoon of sesame oil. Add tofu, shredded cabbage, and carrot, and cook, stirring, for a minute.
Add grated ginger and garlic, soy sauce, remaining sesame oil, and cornstarch. Mix and sauté until sauce has thickened and vegetables have softened. Remove from heat and mix in chopped spring onions. Set mixture aside.
Prepare a dipping station with a tray of water and a wet work surface. Dip a rice paper sheet in water for a few seconds and place it on a damp surface. Add a large spoonful of mixture and wrap the sheet into a rectangle from bottom to center, then top to center, and fold in the sides. Dip a second sheet of rice paper and double-wrap the dumpling seam side down for an even thickness. Place on an oiled plate.
Repeat this process for the remaining filling (or sheets).
Pan fry dumplings in some oil on medium heat in two batches for 3 minutes on each side or until crispy and lightly golden.
Serve hot with dipping sauce. Enjoy the best rice paper dumplings!