Place stock ingredients in a large soup pot, cover, and bring to a boil on medium heat. Lover teh heat and simmer for 45 minutes.
Meanwhile, slice the tofu into small, bite sized cubes and set aside in baking dish. Combine the ginger, garlic, chilies, oil, and 2 tbsp of the soy sauce in a heavy skillet, saute for a few seconds, and then add the tofu. Gently toss until evenly coated. Bake for 25 minutes, stirring twice to roast evenly. Remove the chili halves.
Strain the stock into another soup pot. Add the baked tofu and the carrots and peppers, and simmer for 3 to 4 minutes. Stir in the shredded greens. When the soup returns to a simmer, remove from the heat and add the sesame oil and the remaining 1/4 cup soy sauce.
Serve immediately, scattering freshly sliced scallions into each bowl.