public with sharing class BusinessException extends Exception
{
    public static void recordError(String fileName, String methodName, String errorMessage)
    {
        Exception__c newException = createError(fileName, methodName, errorMessage);
        insertError(newException);
    }

    private static Exception__c createError(String fileName, String methodName, String errorMessage)
    {
        Exception__c result = new Exception__c();
        result.FileName__c = fileName;
        result.MethodName__c = methodName;
        result.SystemError__c = errorMessage;

        return result;
    }

private static void insertError(Exception__c oopsey)
{
        try
        {
            insert oopsey;
        }
        catch(DMLException dmlError)
        {

        }
    }
}

try
{
   //something
}
catch(QueryException error)
{
    BusinessException.recordError('File_Name', 'Method Name', error);
}