As an alternative to stovetop toasting, the sesame seeds can be toasted in the oven. Preheat oven to 350 degrees Fahrenheit. Spread the sesame seeds on a rimmed baking sheet and toast. Stir the seeds one or two times until they are fragrant, about 5 minutes. Transfer the toasted sesame seeds to a large plate or tray and let them cool completely.
If tahini separates, stir the paste to redistribute the oil.
One tip to get a smoother tahini at home is to by grinding the seeds before adding the oil.