Slice tofu in half lengthwise (butterflied) to make two thinner layers.
Line a sheet pan or plate with paper towels and place the tofu slices in a single layer on the paper towels.
Add another layer of paper towels to the top of the tofu and place a heavy pot or a weighted down sheet pan on top.
Allow the tofu to be pressed under the weights for 30 minutes.
Once pressed, remove the weights, discard the paper towels, and dice the tofu into cubes approximately 3/4" to 1" in size. I got about 32 cubes total.
In a large bowl, add the tofu cubes and the cornstarch together. Gently toss, making sure the tofu is well coated in a thin layer of cornstarch.
In a 10" cast iron skillet (or saute pan) with high sides, add the vegetable and sesame oils and heat over medium heat until shimmering, but not smoking.
Carefully add the tofu in a single layer. Turn the heat down if the oil starts splattering or if the tofu is browning too quickly.
Cook nuggets until golden brown on all sides, about 6-7 minutes per side. You'll know the tofu is ready to turn when it releases easily from the pan. If the tofu sticks when you try to turn it, give it another minute to cook and it should flip easily.
Once fried, remove cubes from the pan and drain on a plate lined with paper towels for a minute or two.
While the tofu drains, add the hoisin sauce to a large bowl.
Add the warm tofu to the bowl of hoisin and toss until well coated.
Transfer tofu to a serving plate and garnish with chopped peanuts, cilantro and scallions. Serve with additional hoisin sauce for dipping.