Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper for easier cleanup.
Cut the tofu into bite-sized cubes and place them on the prepared baking sheet. Drizzle with vegetable oil and sprinkle with cornstarch. Toss until evenly coated, then season lightly with salt and black pepper.
Spread the tofu into a single layer and bake for 18 to 20 minutes, or until the edges are golden and lightly crisp.
While the tofu bakes, prepare the sauce. In a medium bowl, whisk together the peanut butter, soy sauce, lime juice, honey, and garlic until smooth. If the sauce is too thick, stir in a tablespoon of water at a time until it reaches the desired consistency.
Taste the sauce and adjust the flavor if needed by adding extra lime juice, honey, or soy sauce.
Remove the tofu from the oven and transfer it to a large bowl. Pour the peanut sauce over the tofu and gently toss until well coated.
Divide the cooked rice among serving bowls and arrange the steamed broccoli alongside the tofu.
Finish with a sprinkle of sesame seeds and sliced scallions before serving.