In a bowl, soak shiitake mushrooms in hot water for 30 minutes until softened, set aside.
Slice tofu lengthwise. In a well-oiled frying pan, pan-fry on both sides until golden brown.
Remove stems from the mushrooms. Chop the mushrooms into very small pieces (~¼-inch).
Cook carrots in a microwave for 2 minutes or steam until softened; mash with fork.
Chop up celery into tiny pieces (~¼-inch).
Oil a large frying pan or wok, add in mushrooms, carrots, celery and soy sauce. Stir fry for about 5 minutes until vegetables are softened.
Turn off heat and add in sesame oil, mix well.
Put 2 teaspoons of the prepared filling on each dumpling wrapper. Lightly wet the edge with water using your finger; close it in half while pinching the edges together. Make pleats and press to seal the edges well.
Pan-fry the dumplings until skin is golden brown on all sides; enjoy while it's hot!