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To build the levain: In a large bowl, mix the starter, flours, and water until incorporated. Cover and leave in a warm place (about 75°F) for 3 to 4 hours, or until doubled in size. You can use your levain immediately or refrigerate it up to 12 hours (or overnight) to use the next day.
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To make the dough: Add 280g of the water to the levain in the bowl. Stir to partially dissolve the levain; it’s OK if it’s not fully combined.
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Add the flours, sugar, and olive oil and mix until there’s no dry flour left. Cover the bowl and let the dough rest in a warm place for 1 hour.
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Add the salt and the remaining 70g water.
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Squeeze the dough with your hands to work the water and salt into it; try not to tear it. This process should take 3 to 5 minutes.
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Take the dough out of the bowl and perform a slap and fold or some stretching and folding to build strong structure; a bench knife is a handy tool here.
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Once you can handle it a bit more easily, stretch and/or knead your dough until its surface is smooth. Return it to the bowl, cover, and let it rest for 30 minutes.
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Perform a stretch and fold to continue building strength. Repeat this process one more time for a total of two stretch and folds in a 1-hour period.
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Allow the dough to rise for 4 to 6 hours. It should be nice and bubbly to the touch; if it’s in a clear bowl you’ll see a web-like structure near the bottom.
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Place the dough on a floured work surface. Pat it into a rectangle and fold from the top to the center a few times to create a loose cylinder.
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Place the dough on a baking sheet coated with olive oil, then coat the dough itself with olive oil. Cover and refrigerate for 12 hours.
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An hour before you’re ready to bake, start preheating the oven to 450°F to 500°F.
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To prepare the toppings: First, make the brown butter by sautéing the butter in a saucepan on medium heat until it turns golden brown. Remove the pan from the heat and let the butter cool for 15 minutes.
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Use your hands to gently coat the dough, which will have spread and flattened on the pan, with almost all the brown butter (reserving some to use just before baking).
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Use your fingers to dock (dimple) the dough, making an even pattern of peaks and valleys. You’ll want to be relatively gentle and not poke holes through the bottom.
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Slice the fruit into very thin slices (16ths are good) and arrange the slices evenly on the focaccia, aiming for at least one slice per serving. Top with the sliced almonds, sprinkling them over the dough and fruit. Drizzle honey (to taste) on top, along with the remaining brown butter.
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Bake the focaccia for 20 to 30 minutes (depending on how hot you've preheated your oven), or until it’s slightly darker than golden brown. It's at its best when it’s crispy on the outside and chewy on the inside.
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Remove the focaccia from the oven and transfer it to a rack to cool slightly before serving.
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Store leftover focaccia, lightly wrapped, at room temperature for a day or so; wrap securely and freeze for longer storage.