My employee mistakenly undercharged a customer and the customer signed the contract. Can we void the order?

This is a complicated question, and likely will depend on how "huge" a mistake was made. The law treats the unilateral mistake (versus mutual mistake) of one party as something that can be fixed in a court action called "contract reformation" provided the non-mistaken party KNEW or HAD REASON TO KNOW of the mistake. For example, if your buyer had reason to know the price was far to low, and took advantage of the situation, then the contract could be re-written by a court to reflect reality. However, if the first the buyer knew of it came from you when you called the buyer, then a court likely will enforce the contract as is.

I would recommend speaking to a commercial lawyer to get a better, clearer picture of the situation you are facing. Whether or not court action would be a good idea depends on how large the mistake is, and whether the risks of litigation, the time and expense of litigation, and the intangible harms associated with suing a customer.

Good luck!

NOTE: This answer is not intended to be legal advice and should not be construed in that way. This answer does not create an attorney-client relationship and no such relationship may be created absent a signed retainer agreement. The author is licensed in Illinois only, and his answer is for educational purposes alone.