Heat oven to 425°F (220°C). Cook rice according to package directions. Press tofu, cut into 1-inch cubes, and toss with 1 tbsp cornstarch, 1 tbsp soy sauce, and 1 tbsp oil. On a sheet pan, toss broccoli and carrots with remaining 1 tbsp oil, salt, and pepper, then push vegetables to one half. Spread tofu on the other half in a single layer. Roast 25 to 30 minutes, flipping tofu and tossing vegetables halfway.

While the sheet pan roasts, whisk together peanut butter, remaining 1 tbsp soy sauce, lime juice, maple syrup, garlic, and ginger. Stir in warm water a little at a time until smooth and pourable.

Divide rice among bowls. Top with roasted tofu and vegetables. Drizzle with peanut sauce and garnish with scallions and sesame seeds. Serve warm.