Move oven rack to middle position and preheat oven to 350 degrees F. Lightly brush 6 cup Bundt pan or 8"x3" ovenproof ring mold with half the melted butter and chill 2 minutes. Butter again with remaining melted butter then chill until pan is needed.
Bring stout to a boil in a small saucepan and add prunes. Remove from heat and let stand until most of the liquid is absorbed.
Meanwhile, sift together flour, baking soda and salt into a bowl. Set aside. Melt the chocolate and 1/2 cup unsalted butter together in a small heavy saucepan over low heat, stirring constantly. Remove from heat and set aside.
Beat together eggs, brown sugar and vanilla in a large bowl with an electric mixer at high speed until thick, about 2 minutes. Add chocolate mixture and beat until just combined.
Reduce speed to low and add flour mixture, mixing until just combined. Stir in prune mixture until combined well. Spoon batter into pan and bake until a wooden toothpick inserted into middle of cake comes out clean, about 40-45 minutes.
Cool cake in mold on a rack 10 minutes, then invert onto rack to cool completely, at least 30 minutes.