Core the tomatoes, cut in half, then cut each half lengthwise into 3 wedges. Then cut each wedge in half crosswise. Place the tomatoes in a large bowl, sprinkle with a pinch of sugar and give them a quick toss.
Cut off the ends of the cucumbers. Using a vegetable peeler, make long stripes going top down. Slice into 1/4" thick slices slightly on the diagonal. Transfer to the bowl with the tomatoes.
Cut the avocado in 4 quarters lengthwise and remove the pit. Gently remove the skin, then slice into 3/8" thick slices on the diagonal and add to tomatoes and cucumbers, along with the diced onion and chopped basil.
To prepare the dressing, throw all of the dressing ingredients into a small bowl and whisk together vigorously, until well blended.
Pour the dressing over the vegetables and toss gently using both hands. You can serve immediately or cover the bowl with a plastic wrap and let sit at room temperature until ready to serve. This salad only gets better with time.