Measure the raw dry sesame. Put it in a glass or ceramic bowl, cover by about 2 inches with warm filtered water, add a small pinch sea salt, cover, and soak 12 to 24 hours.
Drain through a fine-mesh stainless strainer, rinse, and transfer to a clean sprouting jar.
Keep the seeds moist, rinsing and draining daily, until tiny shoots appear, about 2 to 3 days.
Spread the sprouted sesame thinly on a stainless sheet pan and dry at the lowest oven setting until completely dry, loose, and free-flowing. Cool fully.
Combine the sumac, marjoram, thyme, full prepared sesame yield, oregano, sea salt, black pepper, and optional cumin in a dry glass bowl.
Stir from the bottom until the pale sesame and dark herbs are evenly distributed through the red-purple sumac and no soft clumps remain.
Measure 1/4 cup for the Middle Eastern beef stew.
Transfer the remaining za’atar to an airtight glass jar and store in a cool, dark pantry with a clean dry spoon.