You can can almost anything. The safety guidelines have changed over the years though. Used to be that people would can using what is called a "hot water bath" where the jars of food are boiled a certain length of time in a large pot of water, and some would only get the food really hot and throw it in a jar.
The modern guidelines for canning say to only use the hot water bath for very acidic foods and to can everything else using a pressure canner/cooker. They say to never use the method of just heating the food, but some people still do.
I tend to error on the side of safety, so the only thing I have ever canned so far is some salsa and some pickles using the hot water bath method. I am hoping to get a pressure canner this year and experiment with other things.
I do still have one jar of icebox pickles left in the refrigerator that I made last Fall. Those things are awesome!
How To Make Ice Box Pickles
I didn't can these, only put them in a jar and stored in the fridge. They keep a really long time.
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