Heat the oil in a large pot or Dutch oven over medium heat. Add the leeks, celery, and 1/4 teaspoon salt and cook 5 minutes, stirring occasionally. Add the mushrooms and cook until soft, 8 to 10 minutes more.

Stir in the tamari, wine, garlic, and thyme and cook for 30 seconds to 1 minute, or until the wine has evaporated. Add the broth and the cauliflower.

Simmer uncovered for 20 minutes, or until the cauliflower is very soft. Transfer to a blender, add the mustard and vinegar, and blend until smooth. If your soup is too thick, add a little bit of water to the blender to reach a creamy consistency. Season to taste and serve with desired toppings.