Start by shredding the cabbage using a box grater. In a mixing bowl, combine the shredded cabbage, crumbled tofu, chopped shiitake mushrooms, minced garlic, grated ginger, chopped basil, and soy sauce. Mix thoroughly until well incorporated.
Lay out a dumpling wrapper on a clean surface. Place about a teaspoon of the filling in the center of the wrapper. Moisten the edges of the wrapper with a little water using your finger. Fold the wrapper in half to create a half-moon shape, and pinch the edges to seal tightly.
In a small bowl, mix together the cornstarch and cool water until smooth. This will be used to create a crispy base for your potstickers.
Heat the cooking oil in a non-stick skillet over medium heat. Once hot, place the potstickers in the skillet, making sure they don’t touch each other. Cook for about 2-3 minutes until the bottoms are golden brown. Carefully add the cornstarch slurry to the skillet, then cover with a lid. Allow to steam for about 5-7 minutes until cooked through.
Once cooked, remove the potstickers from the skillet and serve them hot with your favorite dipping sauce.