Is there a non-violent, practical way of making hydrochloride with only Hydrogen and Chlorine? A way of making HCl gas is to put Chlorine and Hydrogen into a test tube and expose it to UV light.

This reaction is however fast and strong and I would like to store the Hydrochloride from it.

Another way would be to dissolve Chlorine in water, which would make Hydrochloride, but most of it would go in water and make dilute hydrochloric acid. I could however store the HCl fumes from the dilute acid. I do not know about the practicality of this.

What is the best, and exceptionally practical way of making Hydrochloride when the only resources I have are Hydrogen and Chlorine?
The best and practical way is to sell hydrogen and chlorine, and buy yourself some $\ce{HCl}$ (unless it is prohibited in your jurisdiction). However, I would recommend that only if you have some experience in chemistry and understand quite well the dangers thereof.

The technical answer to your question is: build a galvanic cell with platinum anode and graphite cathode, and feed them with hydrogen and chlorine, respectively. It will perform your reaction in a pretty controllable and non-violent way, and also will give you some electricity for free. Not that I expect you or anyone else to be actually doing this, though.

Why would you need gaseous $\ce{HCl}$, really?