Toast sesame seeds in a skillet over medium-low heat for about five minutes. Toasting develops a nuttier and more intense flavor. But be careful! The sesame seeds can easily burn. While toasting them, stir almost constantly. After you toast them, spread them out on a cookie sheet or very large plate to cool. Otherwise they will continue to toast in the pan. (See Note.)
Process the seeds in a food processor for a couple of minutes, until crumbly.
Add the sesame oil (or olive oil). Continue to process. The tahini will become creamier.
Continue to process for several more minutes. It may seem that your tahini will never become creamy when all of a sudden it does. Be patient. It won’t take that long. If after five minutes, your mixture still has a crumbly consistency, add a small amount of additional oil (a teaspoon or so).
If, like me, you don’t love washing your food processor more often than you need to, make hummus in it right after you remove the tahini.