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In the bowl of a stand mixer, dissolve the yeast in the water. Add the honey and stir. Let sit 2 or 3 minutes, until the water is cloudy. Stir in the olive oil.
Combine 3 C of flour with the salt and add it to the yeast mixture all at once. Mix it together using the paddle attachment, then change to the dough hook once the mixture comes together. Knead at low speed for 2 minutes, then turn up to medium speed and knead until the dough comes cleanly away from the sides of the bowl and clusters around the dough hook, about 5–7 minutes.
Turn the dough out onto a clean work surface and knead by hand for 2 or 3 minutes longer. Add flour as necessary until the dough is smooth and elastic. When you press it with your finger it should slowly spring back, and it should not feel very tacky.
Transfer the dough to a clean, lightly oiled bowl. Cover the bowl tightly with plastic wrap, and leave it in a warm spot to rise for 30 minutes, or up to an hour. When it is ready the dough will stretch without tearing as it is gently pulled.
Divide the dough into 4 equal balls. Shape each ball by gently pulling the sides of the ball and tucking them under the bottom, working around the ball 4 or 5 times. Then, on a smooth, unfloured surface, roll the ball around under your palm until the ball feels smooth and firm, about 1 minute. Put the balls on a tray or platter, cover with oiled plastic wrap or a damp towel, and leave them to rest for at least 30 minutes. At this point, the dough balls can be covered with plastic wrap and refrigerated for 1 to 2 days. You will need to punch them down again when you are ready to roll out the pizzas.
Place a ball of dough on a lightly floured surface. Turn the dough as you press down on the center with the heel of your hand, gradually spreading it out to a circle 8″ to 10″ inches in diameter. Alternatively, use a rolling pin to get an even circle. Form a slightly thicker raised rim around edge of the circle. You can transfer the pizza to a lightly oiled pizza pan if you like, or bake it directly on the stone.
When ready to cook, start the Traeger grill on smoke with lid open until fire is established (4 to 5 Minutes). Set the temperature to high and preheat, lid closed, for 10 to 15 minutes.
Salt and pepper the grilled chicken, then toss it with the barbecue sauce and set aside.
In a medium skillet, heat a tablespoon of olive oil over medium-high heat. Add the onion and sauté with a little salt and pepper until translucent, about 2 to 3 minutes. Remove the pan from the heat.
Shape each portion of dough on a flowered work surface into a round disk. Place the shaped dough onto a pizza peel or cutting board with a generous amount of corn meal. Brush the pizzas with olive oil and spread a layer of barbecue sauce on the pie. Sprinkle cheeses evenly over each one and top with the red onions and chicken.
With your grill preheated to high, slide the pizza off the peal or cutting board in one swift quick motion. Bake for 20 to 25 minutes or until cheese is bubbly and crust is golden brown. Carefully transfer the pizza off grill to a cutting board.
Garnish each pizza with cilantro, and green onion. Cut it into slices and serve immediately.
For a couple other pizza ideas try topping with mozzarella, fontina and ricotta cheese and then a mixture of different mushrooms and some black olives.
If you love meat, top with pizza sauce, mozzarella, sweat Italian sausage, pepperoni and some prosciutto ham.
For a quick easy pizza sauce recipe. Add 6 Tbs of olive oil to a sauce pan along with 8 gloves garlic minced. Cook until fragrant and add 1-28 oz can crushed tomatoes. Add some Italian seasoning, red pepper flakes and salt and pepper to taste and simmer for 1 hour. Cool sauce before putting on pizza. Enjoy!