Place eggs, milk, sugar, salt, vanilla, salt, and melted butter in a blender or food processor and blend for 1 minute. Add flour, and pulse several times. Pour batter into a pitcher, cover, and refrigerate for 3 hours, or preferably overnight.
Meanwhile, place prunes, raisins, and 1/4 cup water in a small saucepan over medium heat. Cook until water is almost evaporated. Turn off heat and pour Armagnac evenly over fruit. Using a long, lighted match, ignite the alcohol and stand back until the flame dies out. Pour the fruit and its liquid into a heatproof bowl, and set aside. If using tea, place prunes and raisins in a heatproof bowl and pour tea evenly over fruit. Let cool to room temperature, cover, and set aside.
Place rack in center of the oven and preheat to 375 degrees. Butter an 8-by-2-inch round cake pan, line the bottom with parchment or wax paper. Butter the paper and dust the pan with flour, tapping out any excess. Place the pan on a baking sheet.
Remove batter from refrigerator and whisk to reblend. Forcefully tap the bottom of the pitcher on your work surface to break any top bubbles. Pour batter into prepared pan. Add the fruit, evenly distributing it within the batter; discard any remaining soaking liquid. Bake until top of the cake is puffed and brown and a thin knife inserted into the center comes out clean, 50 to 60 minutes. Transfer pan to a wire cooling rack and cool to room temperature.
To unmold, place a piece or parchment or wax paper over the wire cooling rack and dust with confectioners? sugar. Have your serving plate ready. Run a blunt knife between the cake and the sides of the pan and gently turn cake out onto the prepared rack; quickly invert onto the serving plate. Dust with more confectioners? sugar just before serving.