For any given uncountable cardinal \(\kappa\) with \(\kappa^{{<}\kappa}=\kappa\), we present a forcing that is \(<\kappa\)-directed closed, has the \(\kappa^+\)-c.c. and introduces a lightface definable well-order of \(H(\kappa^+)\). We use this to define a global iteration that does this for all such \(\kappa\) simultaneously and is capable of preserving the existence of many large cardinals in the universe.