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1
In the bowl of an electric mixer, whisk together flour, salt, and yeast. Add in oil and water and mix on low speed with paddle attachment until combined. Switch to dough hook and knead on medium speed until dough clears sides, but sticks to the bottom of the bowl, 5 to 7 minutes. Turn dough out onto lightly floured surface and divide into 4 equal pieces. Transfer to a parchment paper lined baking sheet, brush lightly with olive oil, cover with plastic wrap, and place in refrigerator for at least 1 day and up to 3.
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2
Melt butter in a medium skillet over medium-high heat. When foaming subsides, add onions and cook until completely softened and browned, about 10 minutes. Remove from heat and set aside.
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3
When all the charcoal is lit and covered with gray ash, pour out and arrange the coals on one side of the charcoal grate. Set cooking grate in place, cover grill and allow to preheat for 5 minutes.
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4
and
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5
the grilling grate. Rub chicken thighs all over with barbecue rub. Place on cool side of grill, cover, and cook until meat registers 165u00b0F on an instant read thermometer inserted into the thickest part of thigh, 15 to 25 minutes. Remove from grill, let rest until cool enough to handle, then pull chicken meat into a medium bowl. Discard bones. Toss chicken with barbecue sauce.
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6
Replenish grill with one chimney of lit coals, arranged on one side of the charcoal grate. Stretch dough out to a long oval or rectangle on a surface dusted with flour. Lightly brush dough with extra-virgin olive oil and place on hot side of grill, oiled side down. Cook until bottom is browned and crisp and top side starts to bubble, 1-2 minutes. Remove dough to plate, cooked side up.
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7
Spread dough with 1/4 of the barbecue pizza sauce. Top with 1/4 each of fresh mozzarella, smoked mozzarella, onions, and pulled chicken. Place pizza on cool side of grill and cover. Cook until cheese is melted and dough is cooked through, 4 to 7 minutes. If bottom crust needs better browning, finish cooking over hotter side of grill as necessary. Remove from grill and sprinkle with cilantro. Serve immediately. Repeat with remaining dough and toppings, there should be enough for up to four 12-inch pies.
