Drain the tofu by placing both blocks on top of a large plate with another large plate on top. With one hand under the bottom plate and the other hand over the top, secure the tofu in place and tilt the plates with the tofu in between to drain the excess water into the sink. Set the plates and tofu down with the second plate still on top.
Place a heavy object such as a cast iron pan or a heavy pot on top to squeeze out more water. Let sit for half an hour.
While the tofu is draining, add the cornstarch, salt and white pepper to the bowl and mix thoroughly with a whisk. Add to a large, sealable food storage bag.
When the tofu has reached 20 minutes of draining in the plate, discard the newly extracted water in the sink again. Then use a paper towel to snugly wrap around each block of tofu to remove the even more water. This takes less than a minute. When removing the paper towels, the tofu should be significantly drier than before.
Cut each block of tofu into squares, one at a time. Start by slicing through the middle sideways so that you have a top half and bottom half. Then cut down in the middle lengthwise and then again in the middle crosswise. Then keep cutting the bigger pieces into halves until you get about 1” almost-cubes. It won’t be perfect but that’s all right. Close to perfect is just right!
Add the tofu pieces to the food storage bag with the cornstarch mix. Spread out the tofu by gently shaking the bag so that there is only one layer inside. Then flip the bag carefully a few times until all the pieces are coated with the tofu.
Heat a large frying pan to medium high heat and when hot, add vegetable oil.
When oil is hot, add tofu pieces to the pan in one layer. Make sure to not crowd the pan. You will fry in batches.
Let sit for 2-3 minutes until the bottom is golden. It might stick so use a spatula to remove it. But to flip over, use chopsticks. Tongs tend to be too big for these pieces and chopsticks allow for more control. Fry the pieces until all the sides are a light golden color.
Drain the tofu on a paper towel on a plate for a minute before moving to a serving plate. Season with salt and fresh ground black pepper to taste.