Add sesame seeds to a wide, dry saucepan over medium-low heat and toast seeds, stirring constantly until the seeds before fragrant and very lightly colored, but not brown. Be very careful because the sesame seeds can burn quickly.
Transfer toasted seeds to a baking sheet or large plate to cool completely.
Add cooled sesame seeds to the bowl of the food processor and process until the look crumbly.
Add 3 tablespoons of the oil then process for 2 to 3 minutes more, stopping to scrape down the sides and bottom of bowl a couple of times. Check the tahini's consistency, it should be smooth, not gritty and should be pourable. You may need to process for another minute or so or add more oil, a teaspoon at a time, until the correct consistency is reached.
Taste before adding salt. Process a few more seconds.
Store tahini covered in the refrigerator for up to one month. Stir well before using.