Before baking, preheat oven to 350°F / 180°C / Gas Mark 4
Spread sesame seeds on a shallow baking tray and bake, shaking frequently, until fragrant, 3 to 10 minutes. Do not brown. Let cool.
Put sesame seeds in a blender or food processor fitted with the metal blade. Add vegetable oil. Start with 1/4 cup of vegetable oil, adding more oil if needed. Process to a smooth paste, about 5 minutes. The Tahini should be a paste with a thick pouring consistency.
Tahini will keep stored in a tightly covered jar in the refrigerator for several months. Makes 3 cups.