Core the tomatoes, cut in half, then cut each half lengthwise into 3-4 wedges. Then cut each wedge in half crosswise. Place the tomatoes into a large bowl, sprinkle with a pinch of sugar, salt, and pepper, and give them a quick toss using both hands.
Cut off the ends of the English cucumber. Using a vegetable peeler, make long stripes going top down. Cut the cucumber in half lengthwise, then slice it into 1/4" thick slices crosswise. Transfer to the bowl with the tomatoes.
Peel the onion and cut in half. You will only need to use half an onion in this recipe, so save the other half for other uses. Then slice the onion into very thin slivers crosswise. Then line the slivers together and cut in half, or leave as is.
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.
Line basil leaves into a stack and roll into a tight cigar. Hold the cigar with one hand and slice very thinly with the other hand using a sharp knife. You want to get very thin, long-ish strips of 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. Cover the bowl with plastic and let sit at room temperature until ready to serve. This salad only gets better with time so a several hour wait before consumption would be ideal.