Juice the carrots and ginger in a juicer. If using a blender, blend them with 1/4 cup water and strain through a fine-mesh strainer.
Pour the carrot-ginger juice into a cocktail shaker.
Add orange juice, honey, and coconut water to the shaker.
Fill the shaker with ice and shake for 30 seconds until well mixed and chilled.
Strain the mixture into ice-filled glasses.
Garnish with orange slices and mint leaves.
Notes
The drink stays fresh in the fridge for up to 24 hours. Store it without ice in an airtight container.Double strain the mixture if you want a smoother texture.For extra sweetness, adjust the honey to taste. Replace honey with maple syrup for a vegan option.Add a splash of sparkling water just before serving for a fizzy twist.