Combine the tofu with the oil in a food processor and purée it until it is smooth. Scrape down the sides. Add the mustard, lemon juice or vinegar, parsley and basil or thyme. Pulse to blend until it is smooth. Add the salt and pepper.
Place the dip in a bowl and refrigerate it until you are ready to use it, up to a day.
Serve with fresh raw vegetables bread sticks or chunks of whole grain bread for dipping, or use as a spread on bread or vegetables.