Break the cauliflower into flowerets. Place in a saucepan with one inch of boiling water containing one teaspoon of the salt. Simmer, uncovered, for five minutes. Cover and cook for five to six minutes longer, only until flowerets are crisp-tender. Drain the flowerets and rinse in cold water. Place in a salad bowl.
Combine the oil, vinegar, pepper, basil and remaining salt. Mix well and pour over cauliflower. Add anchovies, capers and olives. Toss lightly. Sprinkle with additional capers, if desired, before serving.