To prepare the tofu, cut the firm tofu into 8 equal pieces. Sprinkle the salt over the tofu and let it rest for about 5 minutes. Using a small spoon, gently scoop out the center of each tofu piece to create a well, reserving the scooped tofu for the filling.
To make the filling, in a bowl, combine the ground pork, soy sauce, oyster sauce, sesame oil, and water, then mix until well combined. Add the reserved tofu along with the carrots and scallions, and mix thoroughly.
To stuff the tofu, spoon the pork filling into the hollowed center of each tofu piece, packing gently to fill. Lightly coat the top and bottom of each stuffed tofu piece with cornstarch.
To pan-fry the tofu, in a pan over medium heat, add the cooking oil. Carefully place the stuffed tofu into the pan with the filling facing up and pan-fry until both sides are lightly golden, about 5 minutes total. Remove and set aside.
To prepare the broth, in a bowl, mix the chicken stock, soy sauce, oyster sauce, and cornstarch until smooth.
To braise the stuffed tofu, in a clay pot over medium heat, add the cooking oil and stir-fry the garlic until fragrant, about 20 seconds. Pour in the broth mixture and bring to a simmer. Add the cabbage, enoki mushrooms, and the pan-fried stuffed tofu, cover, and braise for about 6 minutes until the filling is fully cooked. Garnish with the scallions and serve hot.