Melt the butter in a 5-quart or larger stockpot set over medium heat. While the butter is still foaming, add the parsnips and cook until lightly browned, 7 to 10 minutes (resist the urge to stir too often or they won't brown). Stir in the shallots, garlic, chopped oregano, salt, and pepper and cook until the shallots are very limp and the entire mixture is beginning to brown, 8 to 10 minutes. Add the broth, using a wooden spoon to scrape up any browned bits in the pot. Bring to a boil, reduce the heat to maintain a low simmer, and cook until the parsnips are very soft, 6 to 8 minutes. Remove from the heat and let cool somewhat.

Puree the soup using a stand or immersion blender (you'll need to work in batches if using a stand blender). Return the soup to the pot and stir in the Parmigiano, soy sauce, and lemon juice. Taste and add more salt and pepper if needed. Reheat the soup and garnish each serving with an oregano sprig, if you like.