The "Least Cost Exception Act" amends the Federal Deposit Insurance Act to introduce a significant exception to the existing requirement that the Federal Deposit Insurance Corporation (FDIC) resolve failing insured depository institutions at the least cost to the Deposit Insurance Fund (DIF). This bill empowers the FDIC to choose an alternative resolution method that is not the absolute least costly, specifically when such a choice serves to limit the further concentration of the United States banking system among global systemically important banking organizations (GSIBs) . For this exception to apply, the FDIC, in conjunction with the Board of Governors of the Federal Reserve System and after consulting the Secretary of the Treasury, must determine that the potential additional risks to the DIF are outweighed by the reasonably expected benefits of reducing banking system concentration. The selected alternative must still be the least costly among options that do not involve a GSIB and do not exceed the cost of liquidation. Furthermore, the difference in cost between the chosen alternative and the least costly option involving a GSIB must remain below a maximum threshold, which the FDIC is mandated to establish by rule within one year of enactment. If the alternative involves another entity purchasing assets or assuming liabilities, that entity must agree to pay an assessment to the DIF over at least five years, covering the additional cost incurred. The FDIC is also required to report to Congress within 30 days of utilizing this exception, detailing the economic difference in cost compared to the least costly alternative that would have been chosen otherwise.