Remove the tofu from its packaging and wrap in paper towels. For best texture and flavor results, you’ll want to remove as much excess water as possible. To do this, place the tofu between two plates and lay a can or book on top to create a gentle weight. Leave this setup in place for at least 30 minutes (see notes).
Preheat the oven to 400 degrees F, and line a large baking sheet with aluminum foil or parchment paper. Lightly grease with cooking spray or olive oil.
Slice the tofu into approximately 1-inch cubes. Place in a medium-sized bowl, then toss with the cornstarch until evenly coated. In a small bowl, whisk together the olive oil, soy sauce and honey. Pour over the tofu and gently toss until evenly combined, then spread in a single layer over half the baking sheet.
On the other half of the baking sheet, toss together the broccoli, olive oil, and garlic. Spread into a single layer and sprinkle with salt. Bake for approximately 30-35 minutes, gently stirring and flipping the tofu and broccoli midway through to ensure even caramelization on both sides, and to prevent the tofu from sticking to the pan.
Meanwhile, prepare the sauce. In a medium saucepan, whisk together the soy sauce, sesame oil, water, and vinegar. Place the cornstarch in a small bowl or ramekin and whisk in 2-3 tablespoons of the sauce, then add back to the bowl along with the brown sugar and garlic. Bring to a simmer over medium heat while whisking, and continue cooking until the sauce has thickened. It will have a strong flavor; add a bit more water if desired to lessen the intensity (but keep in mind that the sauce is meant to be used sparingly).
Serve the tofu and broccoli over cooked grain of your choice along with a drizzle of the sauce, some scallions and sesame seeds.
I actually use a small tofu pressing gadget I was sent free to review several years ago, and it does a great job. I’m genuinely a fan. Tofu and broccoli will caramelize best when they’re not overly crowded on the baking sheet. If you don’t have a large baking sheet, you can use two smaller baking sheets placed on the lower and upper oven racks.