Press the tofu: wrap it in paper towels and set a heavy skillet on top for 15 minutes. Meanwhile, whisk the peanut butter, soy sauce, lime juice, maple syrup, ginger, garlic and 2-3 tbsp warm water in a small bowl until smooth.
Pat the tofu dry and cut it into 1-inch cubes. Toss with the cornstarch in a bowl until evenly coated.
Heat 1 tbsp oil in a large nonstick skillet over medium-high. Add the tofu in a single layer and cook 10-12 minutes, turning every 2-3 minutes, until golden and crisp on most sides. Transfer to a plate.
Add the remaining 1 tbsp oil, then the broccoli and bell pepper strips. Stir-fry 4-5 minutes until crisp-tender, adding a splash of water if the pan looks dry.
Return the tofu to the pan, pour in the sauce and toss for 1-2 minutes until everything is coated and the sauce thickens slightly.
Scatter the scallions over the top, squeeze over extra lime and serve right away.