Combine the tequila, lemongrass-kumquat syrup, Floc de Gascone liqueur, lychee puree and habanero bitters in a cocktail shaker, then add ice and shake. Strain into the glass and garnish with the fresh kumquat.
Combine the sugar, lemongrass and kumquats in a small saucepan over medium heat with 1 cup of water. Bring to a boil, then remove from the heat and let cool. Pour everything into a blender and blend on high for about a minute, then pass through a fine sieve and bottle.