"that...that" VS "such...that"

Question

... (Ray's mother)Her dress hung badly on her body as if she had recently lost a lot of weight.

"Ray," she(Ray's mother) said in that whispery conspirator's voice that he had come to dread. "Ray, listen --"

He ducked his head and pretended to tuck in his shirt. ...

I think the use of first 'that' is like 'such': she said in such whispery conspirator's voice that he had come to dread.

So, I'm wondering if the form of "that...that" is common to replace "such...that". How should we understand it correctly here?

Excerpted from the book - "The Long Walk"

Answer 1

The first that is a colloquial use of the demonstrative adjective to refer to something the speaker believes the listener will recognize because the thing referenced is "out there" in the public consciousness

You know that feeling where you could swear something has happened to you before?

Our new Citrus Blitz has that fresh orange taste (that) you want in a soda.

or because the speaker recognizes it from a previous experience and wishes to point out that this is not the first encounter:

There's that sound again.
-- What sound?
That scratching sound, over near the window.

In a story where the narrator reveals the mind of a character, this use indicates that the character recognizes the thing from previous encounter(s).

The second that in your example is the standard connector to a relative descriptive clause. It is modified by another clause "he had come to dread".

The book (that) he took from the shelf was very dusty.

The thing (that) he had in his pocket was the ring.