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Preheat oven to 350°F.
In food processor, pulse butter, 2 cups flour, brown sugar and salt until mixture is crumbly; press evenly onto the bottom of 13 x 9 inch baking pan. Bake in middle of oven 15-17 minutes or until golden brown.
While shortbread crust is baking, prepare topping. In large bowl, whisk together egg whites and granulated sugar. Stir in 1/2 cup flour and coconut; mix well.
Sprinkle chopped chocolate evenly over the hot shortbread crust. Allow to melt slightly; spread evenly with spatula. Drop small spoonfuls of coconut mixture onto chocolate; spread gently.
Bake 25-30 minutes or until top is golden. Cool completely in pan on cooling grid. Cut into bars. Bar cookies keep, covered, 5 days at room temperature.