Bring pot of water to boil. Add basil; cook 10 seconds. Transfer to bowl of ice water, drain, and squeeze dry. Puree basil, ¼ cup oil, and ½ teaspoon salt in blender until smooth.
Heat 1 tablespoon of oil in a skillet over med-high heat. Add onion and garlic, and cook until fragrant and softened (about 30 seconds). Add corn, zucchini, and remaining salt. Cook, stirring frequently, until they start to caramelize slightly, about 8-10 minutes. If too much excess liquid develops, remove from skillet.
Add tomatoes and vinegar; cook until tomatoes start to collapse, about 6-8 minutes.
Drizzle basil oil on vegetables, and stir. Top with goat cheese or avocado if desired. Serve immediately.