Melt butter over low heat in med. saucepan w/ pouring lip.
Meanwhile, place za'atar in muslin spice bag and close.
When butter is melted, Increase heat to med.-low and bring butter to simmer. Immediately reduce heat back to low.
Place za'atar bag in butter. Gently simmer butter, stirring occasionally, until milk solids on bottom reach a pale brown shade, approx. 30-45 min. Remove from heat. Rest 1-2 min.
Meanwhile, line strainer w/ 3-4 layers of cheesecloth. Remove za'atar bag from butter w/ slotted spoon and discard. Pour butter through strainer into heat-safe measuring cup or mixing bowl w/ pouring lip. Stir in salt. Let cool.
Transfer to clean, dry jar and seal. Store in dark pantry or cupboard (or bury underground!) for at least 1 month. Refrigerate after opening. Smen should last for years.