Add the blackberries, water, and pure maple syrup to a saucepan. Cover, and bring to a full boil. Reduce the heat to a simmer, uncover, and simmer until blackberries turn bright pink and the mixture is very fragrant, about 8 to 10 minutes. Remove mixture from heat, add the basil, and replace the cover. Allow saucepan to sit for 5 minutes for the flavors to infuse.

Strain the blackberry mixture into a jar (I like using a small fine mesh strainer), and push the blackberry and basil pulp against the strainer with a spoon or fork to maximize the amount of syrup (and flavor) you get out. Discard the blackberry and basil pulp. Refrigerate the syrup until ready to use (note: if you’d like to reduce the syrup further until it’s thick, simply cook it longer on the stove top before refrigerating. This is certainly an option, although it isn’t necessary).

Add desired amount of fresh blackberries and chopped basil to each glass, then fill with ice. Pour 1-½ ounces of white rum into each glass, followed by 1 ounce of lime juice and 3 to 4 tablespoons (to taste) of blackberry syrup. Fill the remainder of each glass with sparkling water (or soda water), stir, and garnish with lime wedges.