Growing sesame seeds at home? You bet. Sesame is thought to be the very first oilseed crop ever cultivated. Babylonian records from 4,000 years ago mention it. The ancient Egyptians called it Sesemt. Sesame is known as a survivor crop, as it thrives on the margins of deserts, in drought conditions, and in soil that will not support other crops. The seeds, which are instantly familiar, are produced in capsules that sprout from the main stem of a compact, bushy annual plant. Started indoors, and provided with a good hot summer, the plants will produce loads of edible seeds.