Press the tofu to remove excess moisture: line a plate with several paper towels, place the block of tofu on top, cover with two to three more paper towels, then stack three to four plates on top to weigh it down. Drain for 20 to 30 minutes, checking occasionally that the plates stay balanced.
Unwrap the pressed tofu and transfer to a cutting board. Cut into squares or rectangles about 1/2 to 3/4 inch thick, or to your desired size.
Pour the oil into a large skillet and heat over medium-high until shimmering but not smoking.
On a large plate or shallow dish, combine the cornstarch, 1/2 teaspoon kosher salt, and 1/4 teaspoon freshly ground black pepper and mix to evenly distribute.
Working in batches, dredge each tofu piece in the cornstarch mixture, turning to coat all sides and shaking off any excess.
Carefully add the coated tofu pieces to the hot skillet in a single layer without overcrowding. Cook over medium-high heat for about 10 minutes total, turning occasionally so all sides become golden and crisp.
Remove the tofu from the pan and transfer to paper towels to blot any excess oil.
Season to taste with additional salt and pepper if desired, then serve as desired.