In a large mixing bowl, add cabbage, tofu, mushrooms, garlic, ginger, basil and soy sauce. Mix well.
Prepare the cornstarch slurry: whisk together the cornstarch and water in a small bowl.
To wrap: Place a potstickers wrapper flat in one hand. Place 1 heaping teaspoon of the potstickers filling mixture in the middle of the wrapper. Dip a finger in the slurry mixture and paint along the outside of the wrapper. Fold over to a half-moon shape. Pinch along the outside of the wrapper to close the wrapper completely around the mixture.. Repeat until all potstickers are filled and closed.
Lay folded potstickers in a single layer. Cover with plastic wrap to keep them from drying out. (See headnote re: freezing)
When ready to cook, in a non-stick skillet, heat 1 tablespoon of oil over medium high heat. When the oil is hot, add potstickers in a single layer along the bottom of the pan. Cook until browned on one side, about 2 minutes. Flip and brown the other side equally.
Using the pan cover as a shield from splattering, add 2 tablespoons of water to the pan and cover immediately. Steam potstickers for 3-4 minutes. Uncover skillet, you should see almost all of the water has evaporated. Remove potstickers, then wipe pan dry with towel and repeat for remaining batches.