Cut the head of cauliflower into quarters, then trim out the inner core from each quarter. Break apart the cauliflower into large florets with your hands.
Transfer the cauliflower to a food processor. Process the cauliflower, in small batches, in 1-second pulses until it has completely broken down into couscous-sized granules. (Alternatively, grate the florets on the large holes of a box grater.)
Some florets or large pieces of cauliflower might remain intact. Pull these out and set them aside. Transfer the cauliflower couscous to another container and re-process any large pieces.
Heat olive oil or butter in a large skillet over medium heat. Stir in the couscous and sprinkle with a little salt, if using. Cover the skillet and cook for 5 to 8 minutes, stirring occasionally, until the couscous is as tender as you like. Use or serve immediately, or refrigerate the couscous for up to a week.