How to Make It
Peel cucumbers; reserve peels. Cut cucumbers in half lengthwise; remove and reserve seeds. Cut cucumbers into 1/2-inch slices (about 4 cups); set aside. Cut tomatoes in half lengthwise; remove and reserve seeds. Cut tomatoes into 3/4-inch pieces (about 5 cups).
Combine 1 1/2 cups chopped tomatoes, lime juice, basil, garlic, and 2 tablespoons vinegar in a blender. Add reserved tomato seeds, cucumber peels, and cucumber seeds. Process until smooth, about 30 seconds. Line a fine wire-mesh strainer with a double layer of cheesecloth. Pour mixture through strainer into a medium bowl; discard solids. Season dressing with salt to taste.
Combine onion, 1/4 teaspoon salt, and remaining 2 tablespoons vinegar in a large bowl; toss to coat. Add bell peppers, reserved cucumber slices, remaining chopped tomatoes, and remaining 1 teaspoon salt; toss to combine. Stir in tomato-cucumber dressing. Let stand for 20 minutes, stirring occasionally. Drizzle with oil, and season with salt to taste. Garnish with basil. Serve salad using a slotted spoon.