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Dissolve the sugar in the warm water. Then sprinkle the yeast over the top. Allow that to sit and activate for 5 minutes. The yeast should begin to look kind of foamy, a good sign. That means it's doing its job. If your yeast doesn't seem to change at all (doesn't foam), check the expiration date on your container of yeast.
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In a large bowl stir together the flour, salt, yeasty water mixture and olive oil until a soft dough ball forms. Sprinkle your counter with flour and knead 3-4 times. Lightly oil your bowl (you can use the same one) and return the dough ball. Cover with a clean kitchen towel or plastic wrap and allow to rise in a warm, draft-free spot for about an hour or until it has nearly doubled in size.
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Cream together the butter and sugar. The mixture should begin to lighten in color. Stir in the egg and vanilla extract. In a separate bowl whisk together the flour, baking soda and salt. Stir the flour mixture into the butter mixture. Stir in the chocolate chips. Refrigerate until you're ready to use it.
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Once the (crust) dough has risen, roll out until very thin. Bake at 375°F for 5 minutes while you get the cookie dough ready. It's good to give the bottom crust just a little head start like this because we'll be adding a dense, moist top layer to it with the cookie dough. So it allows the inside to bake some before then. I also think a pizza stone comes in really handy for this recipe, as it helps the bottom crust stay crispy. But if you don't have one, that's OK too.
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Use your clean hands to smash the cookie dough into a large disc, just smaller than the crust. Do this on a piece of plastic wrap. Once the crust has baked for 5 minutes, remove from the oven and carefully flip the cookie dough over the top, peeling off the plastic wrap before popping it all back in the oven. Bake for another 18-20 minutes until the edges begin to brown. Allow to cool for 5 minutes before slicing into it.