Add the lemongrass and ginger to a pan with a tight fitting lid. Add water just to cover and bring to a boil. Place the lid on the pan, remove from the heat, and let steep for 10 minutes. Strain well. Measure 1 cup of the lemongrass + ginger tea (reserving any additional tea for later batches of cough drops.)

Lay out whichever molds you plan on using on a rimmed, heat-proof baking pan.

Add the 1 cup of lemongrass + ginger tea to a large, heavy-bottomed pot over medium-high heat. Stir in the sugar and honey, add the candy thermometer to the bottom of the pan, and stir until the sugar is dissolved. Bring the mixture to a boil, stirring well (avoiding the sides of the pot) from time to time. Watch the candy thermometer. When the mixture reaches about 250°F, stir almost constantly, taking care to stir up the bottom well and still avoid the sides. When it reaches 302°F, carefully pour into silicone molds or a confectioner's sugar mold. Let cool several hours or overnight before unmolding. Toss with confectioner's sugar if desired. Store in a single layer in an airtight container at room temperature.