Preheat oven to 350 degrees. Line bottom and sides of an 8-inch square baking pan with foil, leaving a 2-inch overhang.
Combine chocolate and oil in a medium heat-proof bowl. Set bowl over a pan of simmering water; stir until chocolate has melted. Remove from heat; whisk in sugar, egg, egg white, prune puree, vanilla, and salt until smooth.
In a medium bowl, combine flour and cocoa. Stir into chocolate mixture just until incorporated.
Spread batter in prepared pan. Bake until top is firm and a toothpick inserted in center comes out with a few moist crumbs, 40 to 45 minutes. Cool completely in pan. Using foil, lift brownies from pan. Peel off foil. Using a serrated knife, cut into 12 rectangles.