Heat the oil in a medium pot over medium heat. Add the onion, ½ teaspoon salt, and ¼ teaspoon pepper and cook, stirring occasionally, until tender, 6 to 8 minutes. Add the broth, parsnips, squash, and 1 cup water and bring to a boil. Reduce heat and simmer until the squash is tender, 12 to 15 minutes. Working in batches, puree in a blender until smooth. Stir in the lime juice.
Serve topped with the yogurt, lime zest, and pepper.
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