Gomme syrup is a simple syrup made with the addition of gum arabic, the resin from an African tree. Gum arabic acts as an emulsifier and texturant, providing mouthfeel to cocktails and subtle flavor. It also allows heavily concentrated simple syrups to be kept without crystallization.
In the 19th century, the use of gomme syrup was much more prevalent than it is today. Many people feel that simple syrup can be substituted for gomme syrup.
Gomme syrup does not handle high proof spirits well, turning them milky and lending them an off mouthfeel.
A good starter recipe for making Gomme syrup is to take .5 ounces of gum arabic crystals and crush them in a mortar and pestle to a fine powder. Then take 1 ounce of hot water, pour it over the powder in a small bowl, and wait two hours. Make a strong simple syrup out of six ounces of sugar and 2 ounces of water, bring it to a boil, then add the gum arabic mixture. Bring back to a boil and cook for one minute, skimming any scum that forms. Let the syrup cool. then strain and bottle.
Chris Amirault's recipe for gomme syrup is as follows (posted from eGullet with the author's permission)
Have settled into a recipe that combines the insights here. It's for ~750 ml, as I'm making it for a bar.
With an immersion blender, combine until smooth:
120 g gum arabic powder
150 ml hot (200F) water
(Don't worry about a few lumps.) Then, with the same immersion blender, combine until smooth:
230 g cane sugar
230 g demerara sugar
230 ml hot (200F) water
Combine the two syrups with a bit more immersion blending. Fine strain into a clean bottle.