Set a large saucepan or medium soup pot over medium heat. Add the olive oil. When hot, add the onions, carrots, and celery. Cook, stirring occasionally, until tender, about 8 minutes. Add dried thyme (if using fresh, wait until you add the broth to add the fresh thyme), 1/2 teaspoon kosher salt, and 1/4 teaspoon freshly ground black pepper. Add the flour and cook, stirring constantly, for 3 minutes.
Slowly drizzle in the vegetable broth, stirring to lift the brown bits. Add the potatoes, mushrooms, and if using fresh thyme, add it now. Bring to a boil, then reduce heat to low. Cover and simmer until the potatoes are tender, about 15 minutes.
Remove soup from heat and remove the lid. Let cool a bit. If you used fresh thyme, remove the stems. Remove 4 cups of soup from the pot (I ladle it into a large 4-cup liquid measuring cup). Pour the 4 cups of soup into the pitcher of a blender (or you can puree it with an immersion blender).
Return pureed soup to the pot and stir to combine. Add soymilk. Return to a simmer. Stir in red wine vinegar. Taste and add additional salt and pepper if desired.
Ladle into soup bowls and garnish with parsley, oyster crackers, and/or sliced button mushrooms if desired.