Trim the stem and base of the eggplant. Cut lengthwise in half. Put in large pot of cold water to cover and salt generously. Bring the water to a simmer. Cover and cook for 10 minutes. Drain and cube eggplant. In medium saucepan over medium heat, combine olive oil and garlic. Cook until garlic is fragrant. Add tomatoes, chile, and chopped basil. Bring to a simmer. Lower heat and cook until thickened about 20 minutes. Add eggplant, salt and pepper to the tomato sauce. Add 2 cups water, bring to a simmer and cook for 20 minutes. If the soup is too thick add more water. Place a toasted bread slice in 4 soup bowls. Spoon on the hot soup, sprinkle with cheese and garnish with a basil leaf.