Heat the oven to 350 degrees F. Toss the parsnips, 2 tablespoons olive oil, 1/2 teaspoon salt, and 1/2 teaspoon pepper together and place in a single layer in a baking pan. Roast the parsnips about 60 minutes. Rotate 1-2 times. Trim away any burned areas and set aside.
Heat the remaining olive oil in a large pot over medium-high heat. Add the onion, celery, garlic, 1 teaspoon salt, and 1/8 teaspoon pepper and cook until translucent and softened. Stir in the parsnips, bay leaf, and broth and bring to a boil. Reduce the heat to medium low, partially cover the pot and simmer about 30 minutes. Remove the bay leaf.
Puree the mixture in a blender or with an immersion blender until smooth. If using a blender, return the soup to the pot. Heat the soup over low heat and stir occasionally until warmed through.