Boxwood Hedge Slower to Recover From Pruning Damage Than Rosemary

Q. I have a neighbor concerned about his rosemary and boxwood hedges. The foliage has been falling off. Landscapers recommend he cut them to the ground to get them to recover but he opted to cut them back halfway instead. Now there is a lot of bare wood exposed with no leaves. What should he do to help them recover?

Texas Ranger (Sage) Getting Woody

What should I do and when should I do it?