Blanch red onion in boiling water for 30 seconds. Drain and cool.
Dice cucumber into ½-inch cubes. Remove seeds if using water-heavy varieties.
Halve cherry tomatoes with a knife to avoid juice loss.
Boil 4 quarts water, add 1 tsp salt, then pasta. Cook to al dente (30 seconds under package time).
Reserve ½ cup pasta water. Drain remaining water completely.
In a bowl, combine pasta, blanched onion, cucumber, cherry tomatoes, olives, and basil. Add olive oil while pasta is warm.
Toss gently to coat evenly. Adjust seasoning with salt and pepper. Let rest 1-2 hours before serving.