At what stage should cooking be stopped for both omelette styles before folding?

When the eggs are about 75% set, with just a slight sheen or wetness remaining.

The critical decision in omelette making is stopping the heat application *before* the egg appears fully cooked. If the cook waits until the surface is entirely dry, the lower layer, having been exposed to sustained heat longer, will become tough, potentially rubbery, and likely browned. By stopping when the eggs are approximately three-quarters set—meaning the structure is mostly formed but there is still a visible, slight wetness or sheen on top—the residual heat trapped within the already cooked egg mass is sufficient to gently finish setting the remaining liquid portion after the omelette is folded. This technique ensures the final product retains the intended tenderness, whether creamy French or fluffy American.