In a medium saucepan, heat the oil over medium heat. Add the flour and whisk into the oil, cooking for about 2 minutes or until thick and just lightly browned. Slowly add the vegetable broth, whisking until smooth. Add the potatoes, onion and green onion and bring the soup just to the boil.
Cover and simmer over medium-low heat until vegetables are tender, about 20 minutes. Stir in the watercress and cook until just wilted, about 1 minute. Season to taste with salt and pepper. Purée with a handheld immersion blender until smooth. Divide among six soup bowls and garnish with a dairy-free yogurt and lemon wedges, if desired.