Prepare the tofu: Drain the Extra Firm Tofu (1 block) and place it on a few paper towels; place a few more towels over it. Place a heavy object—like a big frying pan—over the tofu, and let it rest for 10 minutes (and up to 30, if you have the time) to press out the excess liquid.
Heat the oven to 400 degrees F (200 degrees C). Line one rimmed sheet pan with parchment for the tofu, leave another one bare for the broccoli.
Prepare the Broccoli (1 pound): Trim and chop the broccoli into florets. Don't discard the stems: peel off the tough outer skin and knots, then cut the stems into half-inch rounds.
Drizzle Olive Oil (1 tablespoon) over the bare sheet pan, swirl it to coat, scatter the broccoli over top, drizzle with another tablespoon of Olive Oil, season generously with Salt and Pepper (to taste), and toss to coat with your hands. Spread into an even layer.
Remove the tofu from the towels, and cut into one-inch cubes. In a large bowl, gently toss the tofu with Olive Oil (1 tablespoon), the Soy Sauce (1 tablespoon) and the Corn Starch (1 tablespoon) until evenly coated. Spread out on the parchment-line sheet pan.
Cook the tofu and broccoli: Place both sheet pans in the oven and roast for 20 minutes, then toss the pieces around for even coloring and roast another 10 minutes. At this point, the tofu is usually done, which is to say golden at the edges and lightly crisp. Remove the pan from the oven.
Meanwhile make the pesto: Pulse Sesame Seeds (1 tablespoon), Peanuts (1/4 cup), Fresh Ginger (1 1/2 tablespoon), Garlic (1 clove), Soy Sauce (2 tablespoon), Sesame Oil (2 tablespoon), Rice Vinegar (1 tablespoon), Granulated Sugar (1/4 teaspoon) all together in a food processor until ground. Adjust the flavors to taste.
To finish: In a large bowl, combine the broccoli and tofu, and toss with some of the sauce. Garnish with the Scallion (3). Serve Chili Garlic Sauce (to taste), if using, on the side.