Combine ingredients in a medium saucepan and bring to a boil over high heat. Once mixture starts to boil, reduce heat to low, cover and simmer for 20 minutes.
Remove from heat and strain out solids using a strainer or chinois. You will need to fine-strain the mixture, as it still contains quite a bit of the cinchona bark. You can use a coffee filter and wait for an hour or more, or do as I do and run the whole mixture through a French coffee press.
Once you are satisfied with the clarity of your mix, heat it back up on the stovetop or microwave, and then add 3/4 cup of agave syrup to each cup of your hot mix. Stir until combined, and store in the attractive bottle of your choice.
You now have a syrup that you can carbonate with seltzer water; I use my iSi soda siphon for some nicely-textured bubbles. To assemble a gin and tonic, use 3/4 ounce of syrup, 1 1/2 ounces of gin and 2 ounces of soda water over ice.