Well I was actually experimenting with making a sun tea from staghorn sumac berries recently, where I strained the berries to yield a pale pink lemonesque beverage. Somehow, I wanted to include the fuzzy berries, without them being a nuisance to the drink itself...so I froze some of the drink with some of the berries in an ice cube tray: Don't! The basil is too thin and it will oxidize. But your can use herbs with tougher more leathery leaves. Citrus peels will also work well. Since basil leaves are very thin, if you want to use them in an ice cube, it is best to infuse the water first and then remove the leaves before freezing. Using basil in the ice cube itself may look nice for a short time, but the leaves tend to turn a bit slimy when the cube melts. —Sagegreen
a tray of ice cubes
select varietal basil leaves, pineapple, lemon, or sweet basil as appropriate for your drink
Lime and/or lemon rind twists (optional)
filtered water or other beverage for ice cubes
Roll, snip, and bruise the basil leaves into a chiffonade, or work with the whole leaves, depending upon how much flavor you want to impart to the drink. Infuse them in the water. Let these sit until you have enough flavor for your taste. Then remove the leaves. Only if you are working with another herb with tough leaves should you consider leaving the leaf in the water for ice cubes!
Add 1 1/2 cups of basil infused water to an ice cube tray. Add any desired lemon and/ or lime rinds. Then pop in the freezer.
About 4 hours later fill the ice cube tray with the remaining basil water. Freeze solid.
Serve with the liquid of your choice. See some of the options in the photos and consider other choices like those suggested above.