You might be able to find a browning syrup substitute online, admittedly I didn’t search for long. You can buy Parisian essence online at cake decorating ingredients supply places, but it looked a bit pricey to me and I didn’t want to buy something and then not use it. Cheaper to burn sugar in a saucepan! The saucepan cleans up ok afterwards, but I’ll warn you it is a bit stinky to make if you go down that route. If you look up a few recipes you’ll get the gist of what it involves. I didn’t add salt to mine, which some recipes call for. Here’s the method:

Edit: so I had to make the browning syrup, jar it and cool for a day, then make the Nuka cola itself and leave it for a day. I believe there is too much anise in the recipe and not enough vanilla, and I love anise. If you hate anise, definitely use less!