Prepare the ingredients: Cube the honeydew melon, peel and chop the ginger, and juice the lemon.

Combine all solid ingredients into a high-speed blender: the cubed honeydew melon, chopped ginger, and mint leaves (if using).

Pour in the cold filtered water and the fresh lemon juice. Add sweetener now if desired.

Blend on high speed until the mixture is completely smooth and no large chunks of ginger remain. This may take 1-2 minutes depending on your blender.

Taste the mixture. If it is too thick, add a splash more water and blend briefly. Adjust sweetness or lemon juice as needed.

Strain the mixture through a fine-mesh sieve into a pitcher or directly into serving glasses, pressing down on the solids with a spoon to extract all liquid. Discard the pulp.

Serve immediately over ice, garnished with a lemon wheel or a sprig of mint.