add broccoli florets to medium sized pot containing 1/2 inch of boiling water or use steamer insert, cover and steam 3-4 minutes. Drain water from pot, add vinegar, salt, pepper, basil, and oil while still hot. Cool and refrigerate for several hours or overnight. Separate the yolks from whites of cooled, hard-cooked eggs. Set the yolk aside and slice the whites, mixing them with the cooled broccoli mixture. Add the mayonnaise and combine. Spoon mixture into serving bowl. Mash egg yolks with fork and sprinkle over mixture. If desired, sprinkle paprika also.
