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1
Start your pizza dough at least 8 hours ahead of when you want to make your pizza (and up to 2 days). In a large bowl, combine the warm water, yeast, and honey and let stand until the yeast foams, about 5 minutes.
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2
Stir in the olive oil and salt, then gradually stir in the flour until you have a craggy, semi-tacky (but not sticky) dough. Turn the dough out onto a lightly floured surface and knead until it becomes elastic, about 5 to 7 minutes. Transfer the dough to an oiled bowl, cover with plastic wrap or a damp kitchen towel, and let rise in the refrigerator for 8 to 48 hours. Take the dough out of the fridge at least half an hour before using.
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3
In a large pan, heat the butter over medium-high heat until it melts and foams, then stir in the leeks and a big pinch of salt. Cook for a few minutes, until the leeks start to brown, then cover the pan and reduce the heat to medium-low. Cook, covered (but remove the cover and stir occasionally), until the leeks are quite soft, about 10 to 15 minutes. Uncover and add the cream. Turn the heat up enough to bring the cream to a good simmer and cook 1 to 2 minutes, until thickened. Add more salt or pepper to taste, then set aside.
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4
To bake the pizzas, turn the broiler in your oven on high. Place a 12-inch cast-iron skillet on your stovetop and heat it over medium-high heat for about 10 minutes, until it is HOT! In the meantime, on a floured surface, divide your dough into two pieces and use your fingers to press each into a thick circle (you're not stretching the dough quite yet). Let the pieces rest for a couple of minutes while you cut two rounds of parchment paper the size of your skillet. Then, put the parchment on a couple of cookie sheets or cutting boards.
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5
Gently stretch each of your dough pieces into a round that's about the size of the skillet, then place each on one of the parchment circles. Top the first round with half of the leek mixture and sprinkle on half of the Parmesan. Slide this-parchment and all-carefully into the hot skillet (DO NOT TOUCH the skillet without using really good hot pads), crack 2 to 3 eggs over the top, and sprinkle each egg with a pinch of salt.
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6
Transfer the skillet into the oven (remember, it's hot!), directly under the broiler, and cook for about 3 to 4 minutes, until the dough is puffed and deep brown and the egg whites are cooked but the yolks still seem not quite cooked through. Remove the skillet from the oven. Use mitted hands and a large spatula to transfer the pizza to a cutting board. Return the skillet to the stove top and repeat the process to make the second pizza.
