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1
Preheat the oven to 350u00b0F. Line a large cookie sheet with parchment paper, or grease the sheet very well.
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2
In a medium bowl, beat together with an electric mixer the butter, sugar, lemon zest and vanilla. Add the egg yolk and beat to combine. Place a sifter over the bowl and dump in the flour, salt and baking soda. Mix lightly before adding the milk all at once. Beat until just combined-don't over mix.
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3
Use a tablespoon to make 10 cookies on the baking sheet. Lightly press the cookies to flatten them out. Bake for 10 minutes. You may test for doneness by using a toothpick. Let sit on the cookie sheet 3-4 minutes before moving the cookies to a wire rack to cool completely.
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4
In two small bowls, place 1 cup of powdered sugar in each. Add 2 teaspoons cocoa powder to one of the bowls. Add hot water to each bowl and stir vigorously with a fork to form a smooth icing. Start with 3 teaspoons hot water and work your way up to a consistency that's easy to spread but not too runny. Add a few drops of vanilla extract to each bowl. Taste your vanilla icing to see if you would prefer it to have a lemon-y flavor and add lemon juice if you like. Taste your chocolate icing and add another teaspoon of cocoa powder followed by additional hot water, if a stronger flavor is desired.
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5
Traditionally, these cookies are iced on the bottom but I just can't bring myself to do it. On which ever side of the cookie you choose, spread one type of icing on half of the cookie. Let cookies set in fridge for a few minutes before spreading other half with opposite icing-this prevents icing seepage (if you care about that sort of thing). These cookies are best eaten within 2 days because they get soft with age, but if you must store them overnight, I recommend a loose layer of plastic wrap and not an airtight container, which makes for soggy cookies.
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6
One more quick thing: I think these cookies taste best after sitting out for 12 hours or so...something about the icing sinking into the cookie.
