Portuguese carrot soup

4 tablespoons olive oil
1 small onion, coarsely chopped (about 1/2 cup)
1 clove garlic, left whole
1/4 cup peeled, seeded, and coarsely chopped very-ripe tomato
1 pound carrots, peeled, roughly chopped
1 medium white sweet potato, peeled and roughly chopped into 1-inch pieces (about 1 cup)
1 cup peeled and roughly chopped yellow turnip (rutabaga)
4 cups water
1 tablespoon coarse salt or to taste
1/8 teaspoon white pepper

1. Heat 2 tablespoons of the oil in a 4-quart stockpot over medium-high heat. Add and sautй the onion until lightly golden. Stir in the garlic and tomato. Reduce the heat to medium-low. Cover and continue cooking until the tomato is soft and partially dissolved, about 15 minutes.
2. Put in the carrots, sweet potato, and turnip. Pour in the water, cover, and bring to a boil over medium-high heat. Reduce the heat and simmer until the vegetables are very tender, about 30 to 40 minutes. Remove the pot from the heat and puree the soup.
3. Stir in the remaining oil and season with salt and pepper. Bring the soup back to a boil, reduce the heat, and simmer for 2 more minutes and serve.