Scrape the gills out of the portobello mushrooms. Finely chop the portobello and the white mushrooms. Over high heat, heat a stockpot large enough to hold all the ingredients. It is imperative that the pot be very hot before you add the mushrooms. This allows you to cook the mushrooms without oil. Add the mushrooms, garlic, and onion and cook, stirring, for about 5 minutes, until the mushrooms release their water. Don't be concerned if some of the mushroom mixture sticks to the bottom of the pot when you first start cooking it.
Add the wine, water, porcini mushrooms, ¾ cup (180 mL) soy sauce, salt, and thyme and bring to a boil. Remove from the heat, cover, and let sit for 45 minutes. Return to stove and simmer, still covered, for another 45 minutes.
Pour the consommé through a fine strainer twice. Taste and add up to a ¼ cup (60 mL) more soy sauce if the soup needs more seasoning. Reserve 3 cups (720 mL) of the chopped mushroom mixture. Spoon 2 Tbsp. (30 mL) of the mushrooms into individual heated bowls. Ladle 1½ cups (360 mL) of the consommé into each bowl and garnish with a few enoki mushrooms and some green onion rings.