What is this 予以 doing in my sentence?
予以 is a conjunction-like thing that is something like English "as a means of", "for purposes of", and is often used in officialese to keep things comfortably vague. Use it when you are writing a report to your boss.

Postscript:

My answer works when 予以 occurs between two verb phrases.  I would call the phrases I used 'functional equivalents', not literal translations.  

As Shawn's answer notes, 予以 sometimes occurs between noun phrase and verb. In this case, you will have to translate a different way. Here is another example:


有特殊貢獻者應予以表揚
Those who have made special contributions should be recognized.


The grammar used here is literary Chinese, and the original meaning of 予以 as 'give + indirect obj marker' is very clear.  The subject is the direct object, hence in English, the whole thing is passive. Many native speakers don't really know how to use this type of literary construction.