You can use olive oil, sesame oil, sunflower oil, almond oil or any other unrefined and non-hydrogenated oil.
Put the nuts in the freezer in advance, until well cooled. Blend the walnuts with a powerful food processor along with the olive oil.
Optionally, you can use more than the amount of olive oil listed. Begin to blend until you get a smooth paste. If necessary, stop, scoop the mixture off the walls and blend again until you get a smooth nutty tahini.
Season with a pinch of salt and store in a sealed jar in the refrigerator.