Coat the bottom of a large pot with oil and place it over medium heat. When the oil is hot, add the leeks and sauté until softened, about 5 minutes. Add the garlic and sauté until very fragrant, about 1 minute more.
Add soy milk, broth, potatoes and thyme to the pot and give everything a stir. Raise the heat to high and bring it to a boil. Lower the heat and allow to simmer, uncovered, until the potatoes are soft, about 20 minutes.
Transfer ⅓ of the soup to a blender and blend until smooth and creamy, then return it to the pot and stir it into the rest of the soup. Reheat if needed. Stir in the nutritional yeast, hot sauce and vinegar, then season the soup with salt and pepper. Taste test and adjust the seasonings if needed.
Ladle the soup into bowls and top with chives and additional hot sauce. Serve.
I find soy milk gives the best results with this recipe, but you could try swapping out another type of non-dairy milk like almond or cashew, with varied results.