Remove the tofu from its packaging and press between heavy plates and paper towels for at least 15 minutes to remove excess moisture, then cut into 1-inch cubes.
In a small bowl, whisk together the white miso paste, tamari, maple syrup, minced garlic, grated ginger, red pepper flakes, and water until the glaze is smooth and emulsified.
Heat the toasted sesame oil in a large non-stick skillet or wok over medium-high heat until shimmering.
Add the tofu cubes to the skillet in a single layer and sear for 5-7 minutes, turning occasionally, until all sides are golden brown and crisp.
Add the cubed eggplant, broccoli florets, and shelled edamame to the pan with the tofu, stirring frequently for 6-8 minutes until the eggplant is tender and the broccoli is bright green.
Pour the miso glaze over the tofu and vegetables, tossing constantly for 1-2 minutes until the sauce thickens and coats every piece with a glossy finish.
Remove from heat immediately and serve warm in a shallow bowl.