Wash the pennywort leaves thoroughly in several changes of cold water to remove any dirt or grit. Drain well.
Remove any thick stems or damaged leaves, keeping only the fresh, tender leaves and stems.
Place the pennywort, cold water, and granulated sugar into a high-speed blender.
Blend on high speed for 1 to 2 minutes until the mixture becomes completely smooth and vibrant green.
Pour the blended mixture through a fine-mesh strainer or cheesecloth into a large pitcher. Press gently to extract as much juice as possible.
Taste the juice and adjust the sweetness with additional sugar if desired. Stir until completely dissolved.
Refrigerate for 30 minutes until thoroughly chilled.
Pour over ice, garnish with fresh mint or a lime wedge if desired, and serve immediately.