Core, seed and chop the tomatoes into 3/4-inch dice. Peel the cucumber, quarter lengthwise, seed and cut into 1/2-inch pieces. Cut the onion into 1/2-inch dice. Combine all the vegetables in a bowl.
Cut the cheese into 1/2-inch dice, or if using fresh mozzarella, shred it into bite-sized pieces. Add the cheese to the vegetables and toss.
Drizzle the oil over the vegetable mixture and season with salt and pepper. Toss the vegetables with the basil flowers and taste for seasoning. Add a bit more olive oil if the salad is not moist enough. Let the salad marinate at least 30 minutes, and as long as a few hours, before serving. Refrigerate it in hot weather, allowing it to come to cool room temperature for serving.