Cut the first tomato into 4 sticks, try to use the hard parts as much as possible, remove the seeds and loose flesh.
Skewer the sticks with 2 or 3 skewers.
Put the seeds and flesh together with the second tomato, cut into pieces, in a blender and blend until completely liquid. Season with salt and sushi vinegar to taste and then drain through a cheesecloth or coffee filter to get a clear gravy.
Carefully pull the enoki mushrooms apart without removing the bottom, so that you get 2 or 3 flat strips of mushrooms.
Roast the tomato strips over the hot Binchotan until they start to colour nicely and keep them aside.
Now place the grill on the Shichirin and grill the mushrooms on both sides, brushing them with Hoisin sauce while they are cooking.
Place the tomato in the bottom of a bowl with the mushrooms on top, finish off with thinly sliced raw shallot and serve with the tomato gravy.