Add the tea to a 1-quart container with a sealable lid. Pour the vodka in to cover. Cover, and shake gently well to combine. Set aside, shaking gently periodically.
Your infusion should take no more than 10 hours, but possibly less depending on the intensity of flavorings and tannins in your tea. Start tasting within a few hours, and when it reaches a level you like, it's ready.
Meanwhile, make a syrup by combining 1 cup each honey (or sugar) and water in a medium saucepan. Heat over medium-low heat, stirring constantly, until the sugar (if using) is dissolved, and the mixture is well combined and transparent. Remove from heat and cool completely. (Sugar elevates the intrinsic flavors of the tea, whereas honey brings its own character).
Strain the infusion through a coffee filter. Discard the filter and leaves.
Combine the strained infusion and syrup, and stir or shake to blend. Keep in a sealed glass container until ready to serve. Chill if desired, or serve at room temperature.
As this recipe makes about 5 cups, it also makes a nice gift. Simply pour into attractive bottles, and send your guests home with a little sip to enjoy later.