What does “have a pastrami on wry” mean?

I was drawn to the expression, “I wish I could have pastrami on wry“in the beginning sentence of Maureen Dowd’s article, titled “Still mad as hell” in New York Times (February 8):

"I often wonder what Paddy would think. I wish I could have a pastrami on wry with the late writer and satirist at the Carnegie Deli and get an exhilarating blast of truth about “the atomic, subatomic and galactic structure of things today.” What would Paddy Chayefsky make of Kim Kardashian?"

http://www.nytimes.com/2014/02/09/opinion/sunday/dowd-still-mad-as-hell.html?hp&rref=opinion

Though it appears to me the word, “wry” being used as a noun in the above sentence, none of Cambridge, Oxford, and Merriam -Webster English dictionary shows “wry” as a noun.

CED defines it only as an adjective: (before noun) showing that you find a bad or difficult situation slightly funny.”

OED defines it as an adjective:

1. using or expressing dry, especially mocking, humor: example wry smile, wry comments
2. (of a person’s face or features) twisted into an expression of disgust, disappointment, or annoyance.
3. archaic (of the neck or features) distorted or turned to one side:

Merriam-Webster defines it as a verb:

1. (vi) twist, writhe.
2. (vt) to pull out of, or as if out of proper shape :

and adjective:

• humorous in a clever and often ironic way.
• showing both amusement and a feeling of being tired, annoyed, etc.

Here are my questions:

1. What does “I wish I could have pastrami on wry“ mean? Is it a Dowd’s usual lingo? Does “wry” here mean twist or irony?
2. Can “wry” be used as a noun as well as wryness?

Rye is the kind of bread that tastes best with pastrami. "Pastrami on rye" is a common deli sandwich. It's a pun based on the homophonic quality of the words wry and rye, probably chosen because the person the writer is reflecting on had a characteristically dry wit.

Personally, I find it too much of a stretch to be really witty, especially since you have to see it written to understand the joke. On the other hand, the specific location she gives makes it seem like she's referring to something that I am too culturally ignorant to get. Maybe this was a reference to something Cheyefsky had said before with regard to his favorite deli, for instance, and the writer is working in a mention to show her knowledge of and affection for his work.

Pastrami on wry is allusion to pastrami on rye.

And while wry is generally an adjective, it is being used here as a noun to mean something around the definitions:

1. using or expressing dry, especially mocking, humor: example wry smile, wry comments

Here, the pastrami on rye allusion means to eat with and then by extension to enjoy spending time with and delighting in what they can produce. In this case, what he can produce is wry. So she wants to hear how he would mock the stupid things that are happening today.