Coat the bottom of a large pot with the olive oil and place it over medium heat. Allow the oil to heat up for a minute, then add the chopped spring onions. Cook the spring onions for about ten minutes, stirring occasionally, until they soften. Keep an eye on them and avoid letting them brown.
Stir the garlic into the pot and cook it with the spring onions for about one minute, until the garlic starts to become fragrant.
Stir in the white wine. Raise the heat briefly and bring it to a boil, then lower the heat and let the wine simmer until it has reduced by about half, about four minutes.
Stir in the broth and potatoes. Raise the heat to high and bring the broth to a boil. Lower the heat until the broth is cooking at a low simmer. Let the soup simmer for 12 to 15 minutes, stirring occasionally, just until the potatoes are fork tender. Don't overcook the potatoes.
Stir in the spinach and parsley. Continue simmering the soup just until the spinach wilts, which should take a minute or less.
Blend the soup until it is relatively smooth with just a few small bits of veggies. An immersion blender works best for this soup, because it will give you a lot of control and allow you to avoid overblending it. Alternatively, you can transfer it to a regular blender — just be careful not to blend too long or the soup will become gummy. Always be careful when blending hot liquids. Return the soup to the pot if you used a regular blender.
Stir in the lemon juice, then season the soup with salt and pepper to taste.
Ladle into bowls and serve. Optionally, you can garnish each bowl with a drizzle of olive oil, a sprinkle of fresh parsley, and/or some sliced fresh spring onions, if you have any extra.