Bring 2 Tbsp olive oil to medium heat in a large pot. Add onions and garlic, then cook gently for 10 minutes, until onions are soft.
Add salt, pepper, and parsnip to the pot. Stir to coat, then add milk and vegetable stock.
Bring mixture to a slow simmer and simmer 25 to 30 minutes, until parsnip is fork-tender.
While soup cooks, prepare Brussels sprouts. Clean them well then separate the leaves by trimming off the stem. Pluck off leaves then trim more of the stem as needed until you separated as many leaves as possible.
Toss Brussels sprout leaves with olive oil, lemon juice, salt, and pepper, using your fingers to work the oil into the leaves.
Spread onto a parchment-paper lined baking sheet and bake at 350 degrees F (176 C) for 7 to 10 minutes, until the edges of the leaves begin to brown.
Back to the soup. Add white beans then puree (using either a handheld immersion blender or working in batches with a standing blender).
Ladle soup into serving bowls. Drizzle with olive oil and top with crispy Brussels sprouts.