As a verb, shovel is inflected shoveled and shoveling in American English. Outside the U.S., it becomes shovelled and shovelling.
Shovel is one of a large group of l-ending verbs whose inflected forms have lost the double l in American English. Different verbs have lost the second l at different times. Shovel was one of the early changers, with the single-l forms gaining prevalence in the U.S. around 1900. This means that the change is long established and never questioned.