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Preheat oven to 325 degrees F.
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Prepare a cookie sheet by lining it with parchment or a silicone baking mat. (I used a silicone mat and it worked perfectly.)
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Using a stand mixer (or a large mixing bowl), beat butter, tahini, and sugars at medium speed for 2 to 3 minutes, scraping down the sides of the bowl as you do this (Turn the mixer off to scrape down the sides of the bowl or you will have tahini, etc. all over your kitchen!). You want this mixture to be fluffy.
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Add the egg, the egg yolk and vanilla and continue to mix your batter for another minute. Again, scrape down the sides of the bowl as you do this to ensure that the eggs are fully incorporated into your batter.
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In a small bowl, whisk the flour, baking soda and kosher or sea salt together. Turn your mixer on to a low speed and slowly add these dry ingredients to your batter. Next, add the chocolate. Do not overmix.
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Refrigerate your cookie dough overnight in a covered bowl. I found this really did make a difference flavor-wise.
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When you are ready to make your cookies, scoop the batter out of the bowl and form into small balls about 1/2 inch round. Space the dough balls about 3 inches apart. When you have all the dough balls on your cookie sheet, flatten them a bit with the palm of your hand.
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Bake these cookies one sheet at a time. They need careful watching. When they are done, the edges of the cookies will be a medium golden brown and the center of the surface of the cookie will be light colored. The cookies will be soft when you take them from the oven but they will crisp as they cool.
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Bake cookies for 12-17 minutes depending upon your oven. Remove from oven. Cool on a rack for about ten minutes. Sprinkle tops of cookies with coarse salt and dust them with a bit of powdered sugar. The powdered sugar is optional.