Add the sesame seeds to a medium-sized sauté pan and place it over low-medium heat.
Toast the seeds until they are very aromatic and becoming golden brown. This should only take a few minutes -- watch them carefully as they can turn from golden to burnt within seconds.
Pour the toasted seeds into a food processor fitted with the blade attachment. Blend the seeds until a paste has formed. This will take 2 to 3 minutes, and every so often, stop the processor and use a spatula to scrape down the sides.
Add the oil and blend until smooth. You can adjust the amount of oil depending on the consistency you want.
Store in an airtight container in the refrigerator for up to a month.