1. Slice the white and light green parts of the leek into rings. Using a strainer, rinse the leeks thoroughly.
2. In a large pot over medium heat, heat 1 tablespoon of olive oil. Add the leeks, crushed garlic cloves, and a few generous pinches of salt and pepper. Stir and cook until the leeks are soft, about 5 minutes.
3. Chop the broccoli, stems and all, into coarse florets and add them to the pot. Stir and cook until just softened, about 3 minutes. Stir in the white wine vinegar, then add the vegetable broth and coconut milk. Reduce the heat to low and simmer for 5 minutes.
4. Let the soup cool slightly, then transfer to a blender (you can work in batches if you need to). Blend until smooth. Add the spinach and blend again. Taste and adjust seasonings, adding a bit of fresh lemon juice to brighten it up a bit if you like.
5. Garnish with a drizzle of coconut milk and olive oil. Sprinkle with red pepper flakes, if desired.