Cook sesame seeds in a large saucepan over medium heat, stirring constantly, until seeds are toasted and fragrant, about 5 minutes. Remove saucepan from heat and cover with a lid.
Place sugar in a blender and pour in enough water to fill halfway; add seeds. Blend sugar-seed mixture until smooth; pour through a fine-mesh strainer into a pitcher. Repeat blending and straining if a thinner drink is desired, adding more water as desired. Refrigerate juice until cooled, about 1 hour.