Why don't recipes use the word "of" as in "1 cup milk" instead of "1 cup of milk"?

It really confuses me and I can't seem to find the reason for that. It's amazing how it apparently never bothered anyone.

I think it's excluded because it adds no value to the instructions. Historically recipes have either been hand-written or printed which means limited space on a page. Removing words that add no value is a logical efficiency gain (especially when writing by hand). I would guess this approach has just grown to become the standard.

This is just idiomatic English and has been for many centuries. Take for example part of this recipe "[f]or to make gyngerbred" from circa 1400:

Tak & put half a quart hony in a bras panne

(Take and put half a quart honey in a brass pan)

(Via the MED and another site)

That same recipe also calls for you to "tak a pound of pouder gyngere" (take a pound of powdered ginger), so that shows that both forms were used simultaneously.

A similar thing happened with words like “dozen”. The preposition “of” was originally used, for example in “For ix dozen of breede” (For 9 dozen of bread) from 1425. Gradually, this form was replaced by the version without “of” as in “x dosen Curlewes” (10 dozen curlews, a type of bird) from 1450. (Both quotes via the MED.)