Press the Tofu: Drain the tofu and wrap the blocks in a clean kitchen towel or several layers of paper towels. Place on a plate, top with another heavy plate or pan, and weigh down with heavy books or cans. Press for at least 30 minutes to remove as much water as possible. (To skip this step, use super firm tofu from a vacuum sealed package.)
Preheat and Prep Tofu: Preheat oven to 400°F (200°C). Line a large baking sheet with parchment paper. Cut the pressed tofu into bite sized cubes (about 1 inch). Place in a large bowl.
Season Tofu: Drizzle the soy sauce over the tofu and toss gently to coat. Sprinkle with cornstarch and toss again, using your hands gently, until each piece is evenly coated.
Bake Tofu: Lightly spray the parchment lined baking sheet with oil. Arrange tofu in a single even layer. Lightly spray the tops of the tofu with oil. Bake for 25-30 minutes, flipping halfway through, until golden brown and crispy on the edges.
Make Coconut Rice: While the tofu bakes, rinse the rice in a fine mesh sieve until the water runs clear. In a medium saucepan, combine the rinsed rice, 1/2 cup coconut milk, water, and salt. Bring to a boil over high heat. Reduce heat to low, cover, and simmer for 15-18 minutes, until liquid is absorbed and rice is tender. Remove from heat and let steam, covered, for 5-10 minutes. Fluff with a fork.
Make Peanut Sauce: While the rice cooks, combine all peanut sauce ingredients (peanut butter, 1 cup coconut milk, soy sauce, maple syrup, ginger, garlic, and lime juice) in a large skillet. Place over medium heat and whisk constantly until the sauce is smooth, creamy, and fragrant, about 5-7 minutes. Reduce heat to the lowest setting to keep warm.
Combine and Serve: When the tofu is done, carefully add the crispy pieces to the skillet with the warm peanut sauce. Gently stir to coat all the tofu. Serve immediately over bowls of coconut rice. Garnish with cilantro, crushed peanuts, and a lime wedge, if desired. Add steamed greens on the side.