1. Melt butter in a stockpot over medium-high heat. Add onions, thyme, 1 teaspoon salt, and 1/2 teaspoon pepper, and cook until onions are translucent, about 5 minutes. Stir in corn and 4 cups water. Bring to a boil. Reduce heat, and simmer, covered, for 5 minutes.

2. Working in batches, pulse mixture in a food processor or blender until chunky (for a finer consistency, strain half of the mixture through a coarse sieve after pulsing). Thin with up to 1 cup water if desired. Reheat soup before serving. Toss together tomatoes, basil, and oil. Season with salt and pepper. Garnish soup with tomato mixture, and drizzle with oil.