he spoke English so well是一个完整的句子,所以不能用what连接,要用that.
用what的话要是表示一个东西,比如What surprised me was what he brought to me.在这句话里面he brought * to me,其实*当中缺少一个名词,这种情况下,连接才能用what.
而题目的he spoke English so well已经很完整了,句子不缺少成分,所以要用that.