Measure 2 cups of boiling water into a medium Dutch oven set over medium heat.
Put the spinach, kale, and parsley into the pot and stir it into the water so that it wilts slightly.
Add the broccoli, onion, carrot, and garlic to the pot and put a lid on the pot. Simmer for 15-20 minutes, until the onions and garlic are tender (they tend to be the last to soften).
Pull the pot off the heat and let the contents cool for a couple minutes.
Transfer the vegetables and the cooking liquid to a blender carafe. If you have more than fits in your blender, do this in two batches.
Add the nutritional yeast, salt, pepper, and lemon juice.
Holding a towel over the lid of the blender, puree the soup until it is smooth. Add an extra splash of water if it is too thick. Taste and adjust seasoning, if necessary.
Serve warm or chilled, topped with a dollop of plain yogurt or a little coconut milk.