You mean like the Mongols? They didn't stop and farm. Their entire society was built around conquest and pillage.
Their empire was, of course, extremely short, as it collapsed with the death of their Great Kahn soon after it established itself and its following leaders abandoned the previous inroads in the West to focus on the prize of capturing China (that ultimately failed).
Our history tends to focus on the expansion of their empire rather than its subsequent administration, I think in part for that reason.