Prepare the glass: Fill a tall glass with ice cubes.
Muddle the aromatics: Gently muddle the mint leaves and cucumber slices in a cocktail shaker or mixing glass to release their flavors.
Add the citrus: Pour in the grapefruit juice, lime juice, and simple syrup.
Shake or stir: Add ice and shake vigorously for 10-15 seconds if using a shaker. If using a glass, stir well with a bar spoon for 20-30 seconds.
Strain: Pour the mixture through a strainer into the prepared glass.
Add bubbles: Top with soda water and stir gently.
Garnish: Add your choice of garnishes. A grapefruit slice and mint sprig work particularly well.
Serve immediately while the drink is cold and bubbly.