Combine 120 g coarsely ground coffee and 960 ml cold filtered water in a 32 oz mason jar or cold brew pitcher. Stir once to saturate all the grounds.

Cover the jar with a lid or plastic wrap and place it in the fridge. Steep for 16 to 18 hours. Do not steep at room temperature - fridge steeping keeps the extraction slow and clean.

After steeping, strain the concentrate through a fine-mesh sieve lined with cheesecloth or a paper coffee filter into a clean jar. This takes 3 to 5 minutes. The finished concentrate should be deep brown and clear, not murky. Seal and refrigerate until ready to use.

Combine 100 g sugar and 120 ml water in a small saucepan over medium heat. Stir until the sugar dissolves fully, about 2 minutes. The liquid should look clear and you should be able to see the bottom of the pan when you tilt it.

Remove the pan from the heat. Add the basil leaves immediately and press them down gently with a spoon so they submerge. Add the lime zest. Let everything steep for 5 minutes off the heat - the syrup will turn pale green.

Strain out the basil and zest through a fine-mesh sieve. Pour the syrup into a small jar or squeeze bottle and let it cool to room temperature before refrigerating. It keeps for 7 days.

Fill a tall glass with 1 cup of ice cubes.

Pour in 120 ml cold brew concentrate, 60 ml cold filtered water, 2 tablespoons basil lime syrup, and 1 tablespoon fresh lime juice. Stir once from the bottom up.

Taste before serving. Add another teaspoon of syrup if you want it sweeter, or a splash more water if it's too strong. Garnish with a lime slice and two fresh basil leaves if you like.