To prepare the tofu and egg mixture, cut the egg tofu into 1/2-inch pieces and arrange them in a heatproof bowl. In a bowl, add the eggs and salt, then whisk gently until smooth. Add the lukewarm chicken stock and mix to combine. Strain the mixture through a fine mesh sieve into the bowl.
To steam the eggs, in a steamer over high heat, bring the water to a boil, then reduce the heat to low. Place the bowl into the steamer and cover it with a plate, then cover with the lid. Steam for about 15 minutes, until just set. Turn off the heat and let it rest for 1 minute before removing. Depending on the size and depth of the bowl, the steaming time may vary slightly.
To finish and serve, top with scallions. In a small pan, heat the cooking oil until hot, then carefully pour it over the scallions. Drizzle soy sauce over the top and serve immediately.