Prep the ingredients:

1. Wash and slice the lemon and limes in half.
2. Wash and trim the lemongrass, cutting off some of the top leaves. Cut the lemongrass into 2 inch pieces so it will fit your pot. Smash the lemongrass lightly with the side of your knife to expose more of the flavor.
3. Wash and then lightly smash the ginger by covering it with a kitchen towel and smashing it with the side of your knife. 
4. Slice the vanilla bean in half.

Make the syrup:

1. Add the lemons, limes, lemongrass, ginger, vanilla beans, and water to a medium saucepan and bring to a simmer over high heat. 
2. Add the sugar and lower the heat to medium, and simmer very gently for 3 hours until the syrup is reduced by 1/3 and turns a medium amber color.
3. Strain the solids from the syrup and then set aside to cool and store in the refrigerator until ready to use. You will yield about 2 ½ cups of syrup. The syrup lasts for up to 1 month in the fridge.

Make your flavored sugar to rim the glass:

1.  Mix 1 cup of sugar with 1 teaspoon of syrup on a shallow plate.
2. Take one wedge of lime and gently rim the glass you intend to use for your cocktail by swiping the lime across the edge.
3. Turn the glass upside down and press it into the sugar so you have a lip of sugar on the rim of the glass. Repeat with remaining glasses.

Mix the Cocktails:

1. In a shaker or mixing glass, add 1 cup of ice, 2 ounces of lemon ginger syrup, 4 ounces of sake, 1 lemon wedge squeezed, and 1 lime wedge squeezed into the shaker cup.
2. Shake the mixture vigorously for 1 minute. Then gently pour the mix into the prepared glass. Garnish with the candied ginger and serve.