Dr. Stone is an anime with a side of edutainment. It goes out of its way to explain and demonstrate how each of its various inventions and creations works, as well as the science behind them -- with one notable exception: Senku Cola.
When introduced in both the manga and anime, Senku Cola is present post-creation and the audience is given a list of ingredients: lime (including the rind), cilantro, caramel made from burning honey and carbonated water. What has spawned as a result is an era of culinary exploration as the readily-available materials become cannon fodder for experimentation. The method of preparation is up for debate.
From videos to blogs, fans have flocked to the kitchen to try to recreate a piece of the year 5739 in their own homes, and two main preparation methods have arisen. The first method is the "mix-it-up!" method and is the simpler of the two. This method just combines the ingredients straight into a glass and mixes until it has a uniform consistency. Well, it's easy, it's not necessarily good, and it can be tempting to skip the caramelization step and add straight honey instead.
The far more popular method, and the one most commonly seen in videos and recipes, is the "cook" method, which is a little more involved. It begins by chopping the cilantro as small as possible, zesting the lime, adding juice and mixing them with a mortar and pestle. Then, after mixing it in with the caramelized honey, the mixture is strained and the resulting syrup combined with the soda water.
By far the most difficult part of either process is caramelizing the honey, as depending on cookware and experience it can take anywhere from two minutes to over half an hour. Using a frying pan will allow the honey to come to a simmer and "burn" faster, but using a larger pot will prevent spattering and reduce the potential of boiling over, making it safer. Constant stirring and low heat may help ensure an even consistency but at the expense of time. Higher heat may be faster, but the potential for things to go wrong increases easily, and sugar burns are not fun. The best thing to do is to take your experience into account when following, well, any recipe really.
However, just because the "cook" method is more popular does not mean it's correct. Dr. Stone never explains the process behind Senku Cola, meaning that there is a world of experiments just waiting there to find the best possible iteration of the drink. For example, one could experiment with adding any of the other ingredients to the honey as it caramelizes, which may release more flavor... or more flames. Or both! Should the syrup be cooked further after adding the lime-cilantro mix? And what if the entire mixture was added to the soda water instead of just the syrup? Is there a difference between adding syrup to water and water to syrup? Should the lime-cilantro mixture be left to marinate for a few hours? Would there be more flavor with less chopping and processing?
Of course, there's also the issue of ratios. While not as important as in baking, changing the amount of each ingredient changes the flavor and color of the drink immensely. Most fan-made drinks are a golden amber color, as opposed to Senku Cola's deep brown in the anime, which could signify that that most aren't using enough caramelized honey. But, as it's a matter of personal taste, feel free to ignore cannon and play around until you find your favorite combination.
Overall, when it comes to Senku Cola, the best way to make it is to follow the scientific method and really experiment. Try your own methods, take constructive criticism as you force it on your friends, and don't be afraid to fail as you record the results. As Adam Savage once said, "Remember kids, the only difference between screwin' around and science, is writing it down." Until we get a definitive recipe, though, Senku Cola will remain as Dr. Stone's most mysterious invention.