Place 3 cups of water in a medium saucepan and bring to a boil. Turn off the heat, add the tea bags, and steep for 5 minutes. Discard the tea bags, add the prunes and honey, turn the heat to medium-high, and bring to a boil. Lower the heat and simmer uncovered for 3 minutes to plump the prunes.
Pour the prunes and all the liquid into a medium bowl and stir in the Armagnac, vanilla, orange juice, vanilla bean, and cinnamon sticks. With a vegetable peeler, cut 4 large strips of zest from 1 lemon and add to the mixture. Cut the lemon in half, cut 4 (1/2-inch-thick) slices, and add to the bowl. Cover the bowl with plastic wrap and set aside at room temperature for 6 to 12 hours. (If you're not serving the prunes that day, refrigerate them in their liquid.)
To serve, place the prunes in shallow dessert bowls and serve cold, at room temperature, or slightly warmed, spooning the macerating liquid over them. Add a scoop of ice cream, a drizzle of Armagnac, a drizzle of honey, and a sprinkling of grated lemon zest. (You'll be surprised how much flavor this adds!) Serve immediately.