Slice the zucchini in half lengthwise and then make 1/4 inch thick slices crosswise.
Put a heavy bottomed skillet over a medium-high flame and heat the olive oil. Add the garlic and the zucchini and 1/2 teaspoon of the salt. Cool while stirring with a wooden spoon until the zucchini begin to soften. About 7-10 minutes.
Add in the tomatoes, torn basil and the rest of the salt and cook until the tomatoes have broken down, about 10 minutes.
Serve hot or at room temperature. Garnish with more fresh basil.