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