Be careful with this recipe...you won't want to eat any other pizza after this one! 
For the pesto:
1/4 cup pine nuts
3 medium garlic cloves, unpeeled
2 cups packed fresh basil leaves
7 tbsp. extra-virgin olive oil
Salt
1/4 cup finely grated Parmesan cheese 
For the pizza dough:
 ½ cup warm water (about 110°)
1 envelope (2 ¼ tsp.) instant yeast
1 ¼ cups water, at room temperature
2 tbsp. extra-virgin olive oil
4 cups (22 oz.) bread flour, plus more for dusting
1 ½ tsp. salt
olive oil or non-stick cooking spray for greasing the bowl
 
Pizza toppings:
Olive oil, for brushing
Shredded mozzarella cheese
Grilled chicken, cut into bite-sized pieces (about 1/2 of one chicken breast)
Cherry tomatoes, sliced into thirds
Kosher salt and freshly ground black pepper  
Directions for the dough:
Measure the warm water into a 2-cup liquid measuring cup.  Sprinkle in the yeast and let stand until the yeast dissolves and swells, about 5 minutes.  Add the room temperature water and oil and stir to combine.  
Place the flour and salt in the bowl of a stand mixer fitted with the paddle attachment.  Briefly combine the dry ingredients at low speed.  Slowly add the liquid ingredients and continue to mix at low speed until a cohesive mass forms.  Stop the mixer and replace the paddle with the dough hook.  Knead until the dough is smooth and elastic, about 5 minutes.  Form the dough into a ball, put it in a deep oiled bowl, and cover with plastic wrap.  Let rise until doubled in size, about 1 ½ to 2 hours.  Press the dough to deflate it.
To bake, place a pizza stone in the lower third of the oven.  Heat the oven to 500° for at least 30 minutes.  Turn the dough out onto a lightly floured work surface.  Divide the dough into two equal pieces.  Form both pieces of dough into smooth, round balls and cover with a damp cloth.  Let the dough relax for at least 10 minutes but no more than 30 minutes.
Working  with one piece of dough and keeping the other covered, shape the dough  and transfer to a pizza peel or round of parchment dusted with semolina  or cornmeal.  Top as desired.  Slide the dough onto the pizza stone.  Bake until the crust edges brown and cheese is golden brown in spots, about 8 to 12 minutes.  Repeat with remaining ball of dough or freeze for later use.
Directions for the rest: 
To make the pesto, toast the pine nuts in a small skillet over medium  heat until just golden and fragrant, 4-5 minutes.  Set aside.  Add the  garlic to the empty skillet and toast, shaking occasionally, until the  cloves are fragrant and their color deepens slightly, about 7 minutes.   Transfer the cloves to a cutting board; cool, peel and chop.  Place the  basil in a heavy-duty gallon-sized plastic bag. 
Pound the bag with a  rolling pin until all the leaves are bruised. 
Combine the pine nuts, garlic, basil, olive oil and 1/2 tsp. salt in  the bowl of a food processor.  Process until smooth, scraping down the  sides of the bowl as necessary.  Transfer the mixture to a bowl, stir in  the Parmesan cheese, and adjust the salt to taste.  Store in an  airtight container in the refrigerator.
To make the pizza, preheat the oven to 500 degrees F. 
Place a pizza  stone in the oven while it is preheating, and let it heat up for at  least 30 minutes.  Place a round of parchment paper the size of your  pizza stone on a work surface and lightly sprinkle it with cornmeal.   Place the pizza dough in the center and roll it out into a large round  using a lightly floured rolling pin, or a pulling/stretching motion with  floured hands (I use both).  Leave an approximately 1-inch border that  is thicker around the edges for the crust. 
Lightly brush this outer  edge of the crust with olive oil.  Spread a thin layer of pesto on the  pizza crust using the back of a spoon.  Sprinkle with a layer of  shredded mozzarella cheese.  Top with grilled chicken pieces and sliced  cherry tomatoes.  Season with kosher salt and freshly ground pepper, to  taste. 
Carefully transfer the parchment round to the preheated pizza stone.   Place in the oven and bake until the cheese is bubbling and the crust  is lightly browned, about 12-15 minutes.  Slice and serve immediately.  
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