Combine all ingredients in a pitcher and chill.

In a small saucepan, combine the raspberries and water over medium-low heat, stirring occasionally for 10 to 15 minutes, just until the berries completely break down.

Strain through a fine-mesh sieve to remove the seeds (it can be helpful to press the purée with a spatula to extract as much juice as you can!). Chill until cool.

To make the lemonade, combine ¼ cup raspberry juice with the basil in a pitcher; use the end of a wooden spoon to muddle for 30 to 60 seconds. Add the remaining raspberry juice and lemonade. Pour over ice and garnish, if you’d like, with frozen raspberries and/or fresh basil.