Proper Browning as used on damascus barrels is a slow rusting process that entails multiple applications of a chemical solution designed to promote rusting.
Acid based with horrible toxic chemicals like mercury chloride or ferric chloride.
The brown colour is built up after successive passes & removal of the loose rust known as scratching.
There is often a degree of confusion between the processes of traditional browning & bluing as the only difference is with bluing the parts are boiled after each rusting this converts the brown rust ferrous oxide into ferric oxide which is blue!
There are other bluing processes that use a one shot caustic system.