In a small saucepan over medium-high heat, stir together the jalapeno slices, sugar and water for the jalapeno simple syrup. Continue to stir until all the sugar has dissolved and the mixture is simmering. Remove from heat, cover and allow to steep for at least 10 minutes. Taste and let it steep longer depending on how spicy you'd like the syrup to be! Strain and cool completely in the refrigerator before using.
To make the gimlet, add all ingredients to a tall glass filled with ice and stir to combine. Strain into a chilled glass and garnish with slices of jalapeño.