In a pan over medium heat, bring berries and confectioners' sugar to a boil, mashing berries. Let boil for 1 minute. Pour through a fine strainer set over an 8-oz. measuring cup, pressing on solids to extract liquid. You should have about 1/2 cup of puree. Refrigerate until ready to use.
Preheat oven to 350°F. Grease and flour an 8-inch square pan. Place 3/4 cup chocolate chips and butter in a heatproof bowl set over a pan of simmering water and whisk until melted and smooth. Remove bowl from heat; whisk in brown sugar. Let cool, then whisk in eggs and vanilla.
Mix flour, salt and baking powder and stir into chocolate mixture. Stir in remaining chocolate chips. Transfer to pan; smooth top.
Drizzle puree over batter, then swirl a knife through to marbleize. Bake 45 to 50 minutes, until a toothpick inserted in center comes out clean. Transfer to a wire rack to cool completely.
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