Press the tofu cubes between paper towels for a few minutes to remove excess moisture, then set them aside.
In a small bowl, stir together the soy sauce, grated ginger, and honey until the honey dissolves.
Heat the sesame oil in a large skillet over medium heat. Add the tofu cubes and cook for 6 to 8 minutes, turning occasionally, until the edges turn golden.
Pour the soy sauce mixture over the tofu and stir gently to coat. Cook for 2 more minutes so the sauce thickens slightly and glazes the tofu.
Add the edamame and kale to the skillet. Stir and cook for 3 to 4 minutes until the kale wilts but still holds some color.
Divide the cooked quinoa among four bowls. Spoon the tofu and vegetable mixture on top.
Finish each bowl with a sprinkle of sesame seeds and sliced green onions.