I find this to be a fairly deep question, and I think the answer has to do with the methods English has to describe things and the differing syntactic roles that English allows for its parts of speech. I can think of the following ways to describe an honest person.
- By direct modification. English usually puts the modifier before the noun (as you have in "honest woman"). So you may say
My honest secretary is so much so that she never says anything about
- By complementary adjective. That is, by placing the modifier after a copulative verb
My secretary is so honest that she never says anything about my
- By nominative complement, by placing an equivalent noun after a copulative verb. This is the same structure as the complementary adjective, but with a noun instead of an adjective:
My secretary is such an honest woman that she never says anything about my business.
- By action, i.e., by having the person take the characteristic as a direct object of a transitive verb:
My secretary possesses such honesty that she never says anything
about my business.
- By modifying the person's actions, which will require an adverb or adverbial phrase modifying the verb associated with the action.
My secretary operates so honestly that she never says anything about my business.
So let's get to your questions. Why no of in the first formulation? Of is a preposition, and as such requires an object to complete its sense. That object must be a noun, and your chosen word is honest, an adjective. With an adjective, you have to choose either 1 (the direct modification) or 2 (the complementary adjective).
Why is there an of in the second formulation? Your chosen word is now honesty, a noun and you must use the syntax that accommodates a noun. But the choices for a noun don't work. You can't use 3 (nominative complement) because your secretary isn't a quality (honesty); she's a person. You can't use 4 (direct object) because you've chosen is, which is not a transitive verb.
But what you can do is choose 5 (adverbial phrase) by using a prepositional phrase with of to describe the manner of how your secretary is. The preposition requires a noun as its object, and you have just such a word, honesty available.