To make the soup, warm the oil in a large pot over medium-high heat, and saute the oil, onions, and garlic with 1/4 teaspoon of the salt for about 5 minutes until just soft and translucent. Add in the potatoes, tomato, basil, and 1/4 teaspoon of salt, and sauté for about 5 minutes. Add the vegetable broth, and the remaining 1/2 teaspoon of salt, and increase the heat to high, and bring to a boil. Reduce the heat to medium-high, and simmer, uncovered, for about 5 minutes, until the potatoes are just getting tender.