1. Make the peanut sauce; set aside.
2. Drain the tofu, wrap it in paper towels, place a heavy plate on top, and let stand for 10 minutes to press out the excess liquid. Cut the tofu into 1-inch cubes.
3. In a large sauté pan over medium heat, warm the oil. Working in batches if needed, add the tofu cubes and cook until crispy and golden on all sides, about 2 minutes per side. Using a slotted spoon, transfer to a paper towel–lined plate.
4. In the same pan over medium-high heat, cook the shallots and broccolini, stirring often, until tender-crisp, about 6 minutes. Add the bell peppers and cook, stirring often, until all the vegetables are tender, about 4 minutes. Stir in the edamame and soy sauce and cook until the edamame are warmed through, about 1 minute.
5. Divide the rice among 4 bowls and top with the tofu and vegetables. Drizzle with the peanut sauce, garnish with the green onions and peanuts, and serve.