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.
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.
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.
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.
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.