You can also skip making soup and just enjoy the roasted parsnips tossed with the chorizo and caper tapenade.
Preheat oven to 425 degrees. Toss parsnips and onion with 2 tablespoons oil. Season with salt. Spread in a single layer on a rimmed baking sheet. Roast 15 minutes. Flip; roast until golden brown and tender, about 20 minutes more.
Meanwhile, in a small skillet over medium-high, heat remaining 1 tablespoon oil. Add chorizo and cook, turning, until crisp and golden, 2 to 3 minutes. Transfer to a small plate. Reduce heat to medium and add sliced garlic; cook until just golden, 30 seconds to 1 minute. Transfer to plate with chorizo; reserve oil in skillet.
Transfer roasted vegetables to a medium saucepan; add broth, 1/2 cup water, and minced garlic. Bring to a boil, then reduce to a simmer and cook, partially covered, until vegetables are very soft, about 10 minutes. Working in batches, blend until smooth (if necessary, thin with up to 1/4 cup water total). Season with salt and pepper. Just before serving, heat soup through in saucepan over medium-high. Serve, topping each bowl with a few pieces of chorizo and cooked garlic, a spoonful of caper tapenade, and a drizzle of reserved chorizo oil.