In a blender, combine the fresh lemon juice, honey (or agave), and basil leaves. Blend on high speed until the mixture becomes completely smooth and the basil is finely pureed into the liquid.

Strain the blended mixture through a fine-mesh sieve into a large pitcher or glass jar to remove any remaining solids and create a clean, herbaceous concentrate.

Stir in the cold water to dilute and balance the flavor. Cover and refrigerate the lemonade until nicely chilled, at least 1 hour or until ready to serve.

To serve, fill glasses with ice cubes and pour over the basil lemonade. Garnish each glass with a lemon slice and a few fresh basil leaves for a vibrant and aromatic finish.