what deserves us to study in history most is the method (that) our predecessor used to deal with the same events that also happen today.
most这里做状语成分,用来修饰程度的,放在原句的位置上也是可以的,但是从语感角度上说,这样比较好
of是要去掉的,我知道你想用的是of的所有格形式,做定语进行修饰,但是used是谓语动词呀!加上that或者不加,看成是定语从句,先行词是method,that做从句中used的宾语,因而可以省略.
最后的what必须该that,那是定语从句,what不引导定语从句.这是常用考点,切记.