Heat oil in wok. Dip the tofu slices in egg batter and gently place in hot oil. Cook until both sides are brown and then remove and drain on paper towel.
Steam the broccoli florets until just tender and set aside. Squeeze the water out of the soaked mushrooms, remove hard stem and slice into pieces. Trim the ends of the enoki mushrooms.
In a bowl, mix the miso paste, cooking wine, soy sauce and sugar and stir until the sugar dissolves.
Heat a little oil in a pan. Add garlic, carrots, mushrooms and saute for a few minutes. Pour in the sauce mixture, stir and then add water.
Lower heat and gently put the tofu slices in the pan, cover and simmer for 5 minutes. Then pour in the cornstarch mixture and cook until the sauce thickens. Check seasoning, add salt and pepper to taste. Add the broccoli florets and stir . Serve.
The broccoli was added in the end and not while cooking the other ingredients to preserve the green colour.