Cold Query Follow Up Format

I sent a bunch of cold query emails out a little over a month ago and am going to send a follow up email to the people who didn't respond. In sending my cold query I researched proper format, what info to include, time to schedule send the email, etc. In researching the etiquette on follow up emails...there is little beyond whether it is a good idea/how long after do you wait.

My question is what would be the proper format? Send a new email all together or as a response to create a chain with my first email to them? Besides simply saying 'I'm following up on the email I sent', should it just be a rehash of my first email? If responding to my first email do I repeat any of the info already in the chain? Do I send it at a different time than the previous email?

Just looking for general advice on this. I know it's a long shot, cold querying, but I see it as good practice regardless.