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Combine the water, flour, and yeast in a medium mixing bowl. Stir until incorporated. Cover with plastic wrap, place in a warm spot, and let it ferment for 8 hours.
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To caramelize the onions, first remove the peels. Thinly slice all the onions and separate the layers. Heat the olive oil in a medium skillet over medium heat. Add the onions and cover with a lid. Stir often to prevent burning. Cook the onions for about 20-30 minutes until lightly golden. Remove from pan and let slightly cool.
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Add the pecans to a baking sheet and toast them in a 325 degree oven for 5 minutes, until lightly golden and fragrant. Set off to the side.
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In a large bowl, mix the poolish, water, olive oil, yeast, and 1/2 the flour, with a wooden spoon until combined. Add the remaining flour and salt. Mix until combined.
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Turn the shaggy dough out on to a clean surface and knead for 6-8 minutes.
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Add the dough to a lightly oiled large mixing bowl. Cover with plastic wrap and let the dough rise for 1 hour and 15 minutes, until doubled in size.
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Gently turn the dough out on to a lightly floured surface. Cut in half. Shape each half into a round. Place each round on to a cornmeal dusted piece of parchment paper. Cover with plastic wrap. Let it ferment for 50 minutes.
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Preheat the oven to 425 degrees F with two large baking sheets or a baking stone inside the oven.
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When the dough is proofed, gently press dimples in the dough and work it out into a 10 inch round.
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Brush the top with olive oil. Scatter 1/2 the onions, 1/2 the cheese, and 1/2 the pecans on each formed dough.
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Transfer the parchment to the baking sheets and bake the loaves for 15 minutes, until golden. Remove from oven and transfer to a wire rack to cool.