Add mint leaves and sugar to a cocktail shaker. Muddle with a muddler or a spoon until mint is bruised and starting to break up.
Add lime juice, a wheel of cucumber, rum, and ½ cup of ice to the cocktail shaker, shake vigorously until sugar is dissolved.
Fill a highball glass to the top with crushed ice, add a few more mint leaves, a lime wheel, and a cucumber slice.
Strain the mixture in the cocktail shaker into the glass. Top with club soda or tonic water. Garnish with lime wheel, cucumber slice, and a few mint leaves. Enjoy!
Notes
To make this in a glass: muddle the mint and sugar with a cucumber slice, add in some ice, add the rum, add a bit of club soda and stir vigorously, top off with more ice and more club soda.