Forcing lightface definable well-orders without the GCH

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