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Preheat oven to 350 degrees. Butter and flour 8x8x2" metal baking pan.
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Melt chocolate and butter in heavy small saucepan over medium heat, stirring often; cool to lukewarm.
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Using electric mixer, beat sugar and eggs in large bowl until well blended, about 1 minute. Whisk in melted chocolate mixture.
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Sift flour, baking powder, and salt together and fold into batter. Transfer batter to prepared baking pan. Sprinkle walnuts over and press gently into batter.
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Bake brownies until edges are raised and cracked and tester inserted into center comes out WITH some moist batter attached, about 45 minutes.
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Melt apricot preserves in small skillet over medium heat. Strain preserves; brush melted preserves over hot brownies. Cool 1 hour, then transfer to refrigerator and chill until cold, about 2 hours.
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Can be made 3 days ahead. Cover and keep chilled.
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Cut into 16 brownies. Served chilled.