Cut the top 3 inches off of the lemongrass bulbs, using a sharp knife or a pair of scissors. Skewer the pineapple onto these pieces of lemongrass as garnish and reserve.

Slice the remaining stalks very thinly, starting at the bulb end. Place in a medium saucepan with the pineapple juice and the honey and cook over low heat for 15 to 20 minutes.

Remove from the heat, pour into a glass or plastic container, and chill in the refrigerator for about 1 hour.

Place the skewered pineapple in chilled martini glasses. Remove the lemongrass mixture from the refrigerator and add the vodka and lime juice. Stir until well combined and chilled and strain into glasses.