How to dry-brine (i.e. put them in dry salt with very little moisture) vegetables for making mustard pickles?!
Answers: My wife tells me that her mother used to use this method but we can't recall the details; I'm eighty and my wife is not far off so my mother-in-law is unavailable for quesionting.
I think that the technique you are looking for is actually called dry curing, as brining means soaking in a salt water solution.
Now I must admit I had never heard of dry curing vegetables and it took me quite some time to track down a source, but according to "The Encyclopedia of Country Living: An Old Fashioned Recipe Book" by Carla Emery, salting of vegetables can be done thusly:
All root vegetables should be peeled and chunked or sliced. Corn should be removed from the cob, and string beans snapped into sections(no other vegetables are mentioned). You then layer into a crock or other glass or wood container, salt then the vegetables, salt again, more vegetables, repeating until the container is full and ending with a layer of salt. Lay a plate with a weight over the top(something that fits inside the mouth of the container) and then place cheesecloth or other breathable material over the top to keep bugs and such from getting in. It takes about a pound of salt to cure 4 pounds of vegetables. No length of time is given as the following page is missing in the preview I found online. I would assume you could just test them periodically or you could of course purchase the book.