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To make the hemp seed parmesan, add the cashews to a food processor and grind into a powder. Add the hemp seeds, nutritional yeast, sea salt, miso paste, and coconut oil, and process briefly into a paste.
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Place the paste on top of a sheet of parchment paper. Mold the paste into a loose brick, wrap it tightly in the paper, and wrap again with plastic. Freeze the paste for 2 hours, or until it is firm, then move it to the refrigerator to store.
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Use a cheese grater, shaver, or a thin knife to slice the parmesan into thin pieces to serve over the soup. The parmesan softens easily, so wrap it in parchment paper and place in a sealed container.
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To make the broth, slice two of the onions in half and remove only the most papery skin. Slice each half into quarters, while keeping the half together as a unit. Set the cut halves aside. Chop the remaining two onions into smaller pieces and keep them on standby with the other chopped vegetables.
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In a 10-quart stockpot, warm the olive oil over medium heat. Carefully place the sliced onion halves, cut side down, in the oil. Cook for 10 minutes to sear and deeply brown the bottoms—don’t stir or disturb the onions while they are cooking. Add the vinegar and quickly stir together with the onions to deglaze the bottom of the pot. Add all the remaining ingredients, in the order that they are listed, and turn the heat up to bring the mixture to a boil. Reduce the heat to a simmer, and cook for 45 minutes to 1 hour, skimming the top as necessary to remove any foam. Set aside.
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To make the soup, warm the olive oil in a heavy-bottomed pot over medium heat. Add the leeks and cook for 2 minutes to soften. Add the carrots, celery, and garlic and cook for 5 minutes longer, stirring occasionally. Stir in the potatoes and broth. Bring the mixture to a boil over high heat, and then cover and reduce the heat to medium-low. Cook covered for 15–20 minutes, or until the potatoes are soft. Uncover the pot and stir in the peas, lemon juice, and 1/2 cup of parsley. Cook the mixture for 2 minutes longer, or until the peas are bright green and tender, and then remove from the heat. Season the soup with salt to taste.
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To serve, ladle the soup into bowls, drizzle lightly with olive oil, and sprinkle generously with parsley, radish slices, and some hemp seed parmesan.