Engraulis encrasicolus caught and eaten fresh is a small, delicate, mild fish, closer in character to a fresh sardine than to the paste-dark fillet in a tin. The transformation happens in the barrel. Gutted fish are layered with salt under pressure and left, traditionally for several months and often longer.
During that time the fish is not cooked but digested by itself. Enzymes from the fish's own tissue and gut, working in a high-salt environment that suppresses spoilage organisms, cleave muscle proteins into peptides and free amino acids. Glutamate accumulates, which is why cured anchovy reads as deeply savoury and why it disappears into a sauce leaving only depth behind. Colour darkens and texture softens over the same period.
This is why the Roman fish sauce garum and modern anchovy paste belong to the same family of processes. What varies, and is not standardised, is time, temperature, salt ratio and the microbial community involved, and the relative contribution of fish enzymes versus bacteria to the final flavour is still not fully characterised.