Method 1-(Stove-top): Heat a wide, heavy-bottomed skillet over medium-low heat. Add the hulled sesame seeds, toast it, stirring frequently for 5-7 minutes or until it begins to give off a nutty aroma and turns a light golden color. Switch off the heat, and transfer the toasted seeds to a plate. Set it aside until it cools down completely. Method 2 (Oven): Toast the sesame seeds in the oven. Place the sesame seeds on a rimmed baking sheet, in a single layer. Toast at 350° F for about 10 minutes, stirring frequently in between, until the seeds turn a light golden color. Transfer the roasted seeds to a bowl or plate and let it cool to room temperature.
Transfer the toasted sesame seeds to a food processor with sharp metal blades. I used a mini food processor (1.5 cups capacity). If you use a large capacity food processor, you may want to double or triple the batch, so that the seeds are above the blade in order to process well.
Process the seeds until it turns into a coarse paste.
Add oil, a tablespoon at a time to facilitate grinding. Blend after each addition, scrape the sides and the bottom of the bowl occasionally. Stop when you have a smooth, creamy, pourable consistency tahini sauce.
Store your homemade tahini in an airtight container or glass jar in the refrigerator for up to a month. You can store it for longer, but for food safety practices, I suggest using it up within a month. If you do not consume tahini as much, it is best to make a small batch.
If the oil separates and forms a layer on top over a period of time, simply stir the tahini with a spoon.