Toast the sesame seeds over low heat for about 5 minutes until they are fragrant. Make sure to stir constantly so the seeds on the bottom don't burn.
Blend in a high-speed food processor/blender until you obtain the consistency you like. The longer you blend, the smoother and runnier the tahini would be. I like mine very smooth so I blended it for about 7 minutes, giving it a break in the middle so it doesn't over heat.
Store the tahini in a glass container.
Separation of the oil is natural over time, just stir before you use it.
500 grams of hulled sesame seeds yields about 2 cups tahini paste