Pour the hulled sesame seeds into the bowl of a large food processor fitted with an "S" blade, and start processing.
The seeds will take roughly 5 minutes to break down into a crumbly texture, then you can stop and scrape down the sides to make sure everything processes evenly. Process the seeds again, until the tahini becomes silky-smooth. It should take roughly 5 more minutes. (So, 10 minutes total of processing.) You'll hear a change in what the machine sounds like-- the tahini will start to sound more "sloshy" as the seeds release their natural oils.
The tahini is done when it's smooth, with a runny or drippy texture. There will still be a slight graininess when you taste it, but ultimately it will be pretty creamy looking.
Transfer the tahini to a clean 16 ounce jar, and seal it with an airtight lid. Tahini can be stored in the fridge for up to 6 months.