To make the marinade, stir the milk, pickle juice, and hot sauce together in a shallow dish. Add the tofu cubes and gently stir to coat the tofu. Let the tofu marinate for at least 30 minutes, or up to 24 hours. Be sure to cover the dish and place it in the fridge if marinating for longer than 2 hours.
Stir the sauce ingredients together in a small bowl or cup, until the brown sugar completely dissolves. Set this aside.
Whisk the breading ingredients together in a medium bowl.
Very generously coat the bottom of a medium or large skillet with the oil and place it over medium heat. The oil should be about ⅛-inch deep.
While the oil heats up, take a few tofu cubes out of the marinade and add them to the bowl with the breading. Gently roll the tofu cubes around to evenly coat them with the breading.
Once the oil begins to shimmer, start removing the tofu cubes from the breading, one at a time, shaking off any excess breading mixture, then placing the tofu into the skillet. Continue coating and adding tofu cubes, placing them in an even layer so they're not touching. Fry them in batches if needed, for about 4 minutes on each side, until golden and crispy. Add oil to the skillet between batches if needed.
Transfer the tofu to a plate when it comes out of the skillet.
Once all of the tofu has finished cooking, drizzle the tofu with the sauce to coat it, or place it into a bowl and gently toss it. You'll have a bit more sauce than you need.
Serve immediately with extra sauce and any additional accompaniments on the side.