Sauté Aromatics: Heat the sesame oil in a medium skillet over medium-high heat. Add the scallions, ginger, and garlic, cooking until softened and lightly browned around the edges, about 5 minutes. Stir occasionally to avoid burning.
Cook the Chicken (or Mushrooms): Add the ground chicken to the skillet and break it apart as it cooks. Sauté until browned and fully cooked, which should take about 5 minutes. If using mushrooms for the vegetarian version, sauté them until they are golden and tender.
Shred the Tofu: While the chicken or mushrooms are cooking, use the large holes of a box grater to coarsely shred the tofu.
Combine Tofu and Edamame: Stir the shredded tofu, edamame, soy sauce, and salt into the skillet with the chicken (or mushrooms). Cook for about 3 minutes, stirring occasionally, until the mixture is heated through and well combined.
Add Final Touches: Remove the skillet from the heat. Stir in the lime juice and Sriracha to season the dish. Toss in the cilantro and/or mint leaves for a fresh, herbal finish. Garnish with extra scallions and serve immediately.