1. Combine cilantro, onions, garlic, and ginger in a food processor; process until finely chopped. Add 1 cup cabbage and the next 5 ingredients (through kosher salt); pulse 10 times or until finely chopped. Add egg white; pulse until combined. Place cabbage mixture in a medium bowl, and stir in tofu.
2. Moisten edge of gyoza skin with water, working with 1 skin at a time (cover remaining skins to keep them from drying). Spoon about 1 tablespoon tofu mixture into center of circle. Gather up edges of skin around filling; lightly squeeze skin to adhere to filling, leaving top of dumpling open. (If skins do not open enough to see tofu mixture, use the tip of a knife to separate dough and form pockets.) Repeat procedure with remaining skins and filling.
3. Place dumplings in a large bamboo steamer lined with parchment paper or cabbage leaves. Working in batches, steam for 9 minutes or until filling and wrappers are lightly firm. Combine oils, and drizzle over tops of dumplings.