In a small pot, combine sugar and water to make a simple syrup. Cook over medium heat until sugar has dissolved, about three minutes. Set it aside and allow to cool.

Place three strawberry quarters each in four (10-ounce) glasses. Top with two to three mint leaves and one teaspoon fresh lime juice. Using the back of a spoon, gently mull the strawberries, mint, and lime together until they begin to macerate.

Add one to two tablespoons cooled simple syrup and one ounce rum to each glass. Top with sparkling water or club soda. Garnish with lime wedge and additional mint leaves.