The correct answer is: Congress does not regulate an independent agency, the idea of independence itself explains it. It's not necessary. Thoses agencies are created by the congress to work autonomously.
Independent agencies operate outside federal executive departments. Those agencies are constitutionally part of the executive branch and they are free of presidential control. Congress has created a number of independent agencies to help administer several issues of federal government's power and authority. To create an independent agency, it all starts from the Congress, passing a statute granting an agency the authority and autonomy to regulate and control a specific area or industry.