Prepare your glass with a salted rim using juice from a sliced lime.
Dip the edges of the glass in Kosher salt.
Add 2 oz. silver tequila to a shaker with mint and cucumber. Muddle. Strain tequila into a spare glass and remove cucumber and mint.
Return tequila to the shaker with ice. Add 1oz. lime juice and 1 oz. Cointreau. Shake vigorously. Pour margarita with ice into prepared glass and serve.