Preheat the oven to 450°F.

Cut tofu into ½--inch cubes and arrange in a single layer on a clean kitchen towel, place another towel over it, and weigh it down with a plate or baking sheet and a large can on top for 10 minutes (as a press).

While the oven is heating and the tofu is pressing, make the peanut sauce: combine the garlic, peanut butter, soy sauce, lime juice, brown sugar, and red pepper flakes in a blender or food processor. Pulse until smooth, adding water as needed to achieve a pourable consistency.

Toss the broccoli and carrots with one tablespoon of sesame oil in a medium bowl. Arrange them in a single layer on one side of a rimmed baking sheet. Brush the remaining 1 tablespoon sesame oil on the tofu, then arrange it in a single layer on the other side of the baking sheet. Sprinkle a pinch each of salt and pepper over the vegetables and tofu. Place the sheet in the oven.

Roast until the tofu and vegetables are slightly crispy and browned, about 20 minutes.

Serve the tofu and vegetables with the peanut sauce drizzled over the top, and garnish with scallions if desired.