Heat a medium pot over medium-high heat, add 1 tablespoon oil, the scallion whites, and garlic. Cook until softened, 1 minute. Add 7 cups of water, the edamame, and potato; season with salt and cover. Once the soup boils, remove the lid and cook until the edamame and potato are tender, 15 to 20 minutes. Cool slightly and then carefully blend with an immersion until smooth (or in a traditional blender in batches). Keep warm.
Meanwhile, heat a medium skillet over medium-high heat, add the remaining 1 tablespoon oil, then add the mushrooms, ham, if using, and scallion greens. Cook until the mushrooms brown, about 3 minutes, and then add the spinach, stirring until it wilts. Remove from the heat, season with salt and pepper.
When ready to serve, gently reheat the soup and add rice wine vinegar. Ladle soup into 4 bowls and spoon some of the mushrooms, ham, and spinach into each bowl. Drizzle in the hot sauce as desired. Serve.
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