The original manuscript barely shows a supralinear insertion after the verb were. The insert mark is fairly clear in the actual manuscript (but not as visible in the ultraviolet photographs of the original manuscript). The supralinear word is not fully readable but appears to be written. This insertion was probably done later and with very weak ink flow, which suggests that it is a secondary change. It is possible that the word written was introduced into the text when Oliver Cowdery copied the text from 𝓞 into 𝓟. As in 𝓞, this extra word (miswritten as writhen) was also supralinearly inserted in 𝓟; but unlike in 𝓞, it was written with heavier ink flow.
Probably because his attention was drawn to whether written should be added to the text, Oliver Cowdery accidentally changed the plural books to book as he copied from 𝓞 to 𝓟. The original text seems to have read “which were in the books of Moses”, but this ended up being copied into 𝓟 as “which were written in the book of Moses”. The 1981 LDS edition restored the plural books, but the intrusive written has been maintained in all editions. The plural is, of course, appropriate since there are five books of Moses, not one: namely, Genesis, Exodus, Leviticus, Numbers, and Deuteronomy, which are collectively referred to as the Torah (meaning, ‘the law’). The Book of Mormon explicitly states that the plates of brass contained “the five books of Moses”:
Thus “the books of Moses” is correct in 1 Nephi 19:23.
Elsewhere in the Book of Mormon there are a number of occurrences involving the word book (either singular book or plural books) for which the past participle written could theoretically be removed from a passive verb phrase without fundamentally changing the basic sense:
In these examples, the word written is expected but not crucially necessary. Undoubtedly this expectation served as the motivation for later inserting written in 1 Nephi 19:23. Nor is there any evidence that the scribes (in the manuscripts) or the typesetters (in the editions) have ever had diffi- culty keeping written in the text. In other words, there has been no tendency to accidentally delete occurrences of written in those cases where it could have naturally occurred. Thus the lack of written originally in 1 Nephi 19:23 seems to be intentional rather than due to scribal or dictation error.
In support of the original reading in 1 Nephi 19:23, there is one example in the text where written is not used when it could have been:
Theoretically, the text could have been “the truth of the book and the things written therein”. Thus the earliest text for 1 Nephi 19:23 is fully possible and should be restored. The secondary addition of written was unnecessary (although expected). And the use of the plural books is wholly appropriate when referring to the five books of Moses.
Summary: Remove the intrusive written and maintain the plural “in the books of Moses”, thus restoring the earliest form of the original manuscript (“and I did read many things unto them which were in the books of Moses”).