If you don't want to make dumpling dough from scratch, you can buy pre-made dumpling skins at Asian markets in the refrigerated section.
Place flour in food processor bowl. Put top on and turn machine on. Gradually add water to bowl and process until dough forms into a bowl. Continue to process another minute. Transfer to a floured bowl and cover with plastic wrap. Let rest 30 minutes.
Spinach Tofu Filling
Heat oil in non-stick skillet. Add beaten egg to pan and swirl around to make a thin omelet. Cook on one side, then flip over to cook the other side. Transfer to cutting board. Let cool, then finely chop. Put in medium bowl.
Blanch spinach in water or broth; drain let cool. Squeeze dry. Put spinach in food processor and process until finely chopped. You should have about 1 1/2 cups of cooked spinach. Transfer to bowl with egg.
Put tofu in food processor and process until finely chopped (but not pureed). Transfer to bowl with egg and spinach.
Put mushrooms in food processor and process until finely chopped. Transfer to bowl with egg, spinach, and tofu. Season to taste with salt, and stir to mix well. Refrigerate until ready to use.
Divide dough in two. Roll one piece into long rope, using flour to keep from sticking. Cut rope into 14 pieces. Flatten each piece into a circle with the palm of your hand. Roll each piece into a 3" circle.
Place one tablespoon filling on top of each circle.
Pinch center of each side of dumpling together.
Using thumb and forefinger, start to pinch front and back of dumpling skin together on one side of dumpling to seal dumpling.
Do the same on the other side of the dumpling to completely seal in filling.
Set aside on floured pastry mat or plate.
Bring big pot of water to a boil. Add 2 teaspoons salt.
Add dumplings, one at a time, stirring with a big spoon to prevent dumplings from sticking to bottom of pot.
Bring pot to boil. Add 1 cup cold water. Let pot come back to a boil. Add another cup of cold water. Once pot comes back to a boil, remove dumplings with a slotted spoon or strainer.