Peel the plastic off the tofu container (you may need to cut it with a knife) and pour the liquid into the sink. Wrap the tofu with the clean dish towel or paper towels, put it on the cutting board, and put something heavy on top of it — a can or skillet — to press the liquid out. Let it drain for at least 15 minutes, and up to 1 hour.
Cut the tofu into 4 slabs, then cut each slab into 4 cubes.
Turn the oven on and set the heat to 400 degrees. Lightly grease the baking sheet with 1 teaspoon oil.
Put the tofu and cornstarch in the mixing bowl and toss to combine. Add the oil and soy sauce and toss again.
Dump the tofu onto one half of the baking sheet and arrange it in an even layer so that none of the pieces overlap.
Cut the stalk off the broccoli and peel it as best you can. The thick peel will keep the broccoli from becoming fully tender, so remove as much as possible.
Slice the stalk into long, -inch thick pieces. Cut the rest of the broccoli into long, fairly narrow florets (“florets” are the branched clusters at the top of the broccoli).
Put the broccoli in the bowl, drizzle with oil and toss until evenly coated. Sprinkle with the salt and pepper, and toss to combine.
Put the broccoli on the other half of the baking sheet and spread out into an even layer.
Once the oven temperature has reached 400 degrees, carefully put the baking sheet in the oven. Bake until the tofu is deeply golden and crisp on the edges, 20-25 minutes.
Make the sauce while everything is cooking. Put all the ingredients in the small bowl and mix well.
Drizzle the sauce on the cooked tofu and broccoli and mix everything together. Serve right away.