For the syrup, chop lemongrass into small 1 inch pieces. In a small pot, bring water, sugar, and chopped lemongrass to a boil and let simmer for about 20 minutes until mixture becomes a thick syrup.
In a highball glass, muddle Thai basil leaves in cold water and lemongrass syrup. Stir in bourbon.
Add crushed ice and garnish with Thai basil sprigs.