Pre-heat the oven to 375 degrees. Place the cornbread cubes in a large mixing bowl and drizzle with 3 tablespoons of the olive oil. Toss evenly to coat the bread cubes. Spread the cubes in a single layer on a sheet tray and bake until lightly browned and toasted, about 10-15 minutes. Return the cornbread to the bowl and add the tomatoes, cucumbers and onions, if using. Whisk together the 1/2 cup olive oil and red wine vinegar and season with salt and pepper. Drizzle the dressing over the salad. Add the avocado cubes and basil and toss gently. Serve while the cornbread is still warm.