2 cups whole milk
3 large eggs
1/2 cup sugar
5 tablespoons unsalted butter, melted, cooled
1/4 teaspoon vanilla extract
1/8 teaspoon salt
3/4 cup all purpose flour
1 cup small or medium-size pitted prunes (about 6 ounces)
1/2 cup water
1/3 cup raisins
1/4 cup Armagnac or other brandy
Combine milk, eggs, 1/2 cup sugar, butter, vanilla, and salt in blender jar. Blend 1 minute. Add flour and pulse just until blended, scraping down sides of jar. Cover and chill in jar at least 3 hours and up to 1 day.
Combine prunes, 1/2 cup water, and raisins in heavy small saucepan. Cook over medium heat until fruit is softened and water is almost evaporated, stirring occasionally, about 10 minutes. Turn off heat. Pour brandy over fruit. Using long match, ignite brandy. Let flames burn off, shaking pan occasionally. Transfer fruit to small bowl. Cool completely. (Can be made 1 day ahead. Cover and let stand at room temperature.)
Position rack in center of oven and preheat to 375F. Butter 8-inch-diameter cake pan with 2-inch-high sides. Line bottom with parchment or waxed paper. Butter paper. Dust pan with flour, shaking out excess; place on baking sheet.
Reblend batter until smooth, about 5 seconds. Pour into prepared cake pan. Drop prunes and raisins into batter, distributing evenly. Bake cake on baking sheet until sides are puffed and brown and knife inserted into center comes out clean, about 1 hour. Cool cake completely in pan on rack.
Place piece of parchment or waxed paper on flat plate. Sift powdered sugar onto paper. Run knife around cake in pan to loosen. Invert pan onto paper, releasing cake. Remove pan; peel off paper. Place serving plate over cake and invert. Dust top of cake with additional powdered sugar.