Step 1: Preheat oven to 275F (140C or gas mark 1).
Step 2: In a large mixing bowl, cream 1 cup butter and the granulated and brown sugars until fluffy. Add the egg yolk and 1 teaspoon vanilla, mix well.
Step 3: Stir in the flour, cardamom and salt. Spread in an ungreased 10 x 15" baking pan.
Step 4: In a medium mixing bowl, beat the egg white until bubbly but not forming peaks. Brush the dough with the egg white and sprinkle with the chopped nuts.
Step 5: Bake at 275°F for 1 hour.
Step 6: While the bars cool, in a saucepan, melt the 1 1/2 Tablespoon butter until it browns slightly, remove from heat. Beat in 1 cup confectioner's sugar and the 1/2 teaspoon vanilla. Add enough milk to make a "drizzling" consistency. Drizzle on baked cookies. Cut into bars.
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