Drain tofu, wrap in 3 layers of paper towels, and place in a strainer. Add something a little heavy – we used a peanut butter jar – on top, to press. The tofu will mush a bit, that’s OK. Allow to stand for ten minutes. Discard paper towels, chop up pressed tofu and transfer to a food processor.
Grate onion. With clean hands, squeeze out as much water as you can. Measure 2 Tbsp squeezed onion into a food processor, along with egg, soy sauce, and nutritional yeast, if using. Blitz until smooth and well combined.
In a medium-large mixing bowl, combine soy flour, corn starch, garlic powder, pepper, and salt. Add tofu mixture, stir until smooth and well combined. Add edamame and carrot, stir until vegetables are well distributed.
Line two baking sheets with parchment paper. Using two tablespoons, scoop mounds of filling onto the prepared baking sheets – you’ll want rounded Tablespoons, close to about 2 Tbsp in volume. Use a wet finger to smooth mound into a “nugget” about 1.5″ x 2.5″, and about ½” thick. Repeat with rest of batter.
Once all nuggets are formed, transfer pans to freezer and allow to chill until firm.
Once your patties are prepared, heat vegetable oil to 375 F. You can use a deep fryer, or a heavy pan. If not using a deep fryer, use a deep, heavy pot, filled to at least 3″ deep. As oil is heating, prepare your batter:
Whisk together dry ingredients. Add egg and soy sauce, whisk until well combined. Add a small amount of water, stirring to combine. Continue adding cold water, stirring gently until just combined – mixture can be a bit lumpy.
For best results, set bowl of batter in another, larger bowl that is filled with ice. The colder the batter, the better the coating!
Gently dip chilled patties in the batter one at a time, slowly removing from the batter and allowing excess to drip off. Carefully transfer to heated oil. Fry a few at a time – turning every couple of minutes.