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Pat the chicken dry and season on both sides with salt and black pepper. Place a wide, shallow bowl with the flour in it by the cook top. Heat a large skillet (I used a 14 inch) over medium heat. Add the olive oil. When it starts to shimmer, start dragging each piece of chicken in the flour and then knocking the excess off. Place in the skillet. Do not over crowd the pan, you will probably have to do this in batches.
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Make sure the chicken is browned on both sides--this will take a good 10 minutes or more per batch. After each piece is browned, just place it in a bowl or on a plate.
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When all the chicken has been browned, add the onions with a pinch of salt to the pan. Sauté for 5 minutes or so, until softened. Add the garlic and aleppo pepper. Stir and cook for 1-2 minutes.
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Add a splash or two of wine to the pan and scrap up the bottom. If the pan is too dry, add a little more olive oil as well.
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Add the mushrooms with a pinch of salt. Cook, stirring, until they have released their liquid, 5-10 minutes. Keep deglazing the pan as needed with splashes of wine.
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Add 1/2 cup of wine and bring to a boil. Let it boil for a minute or two, then add the chicken pieces, skin side up. Cover and turn down the heat to maintain a gentle simmer. Let simmer for 10-15 minutes, or until chicken is nearly cooked through.
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Then add the second 1/2 cup of wine and bring again to a boil. Stir the asparagus in. Let it simmer briskly until the chicken is completely cooked through and the asparagus is crisp tender and bright green.
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Squeeze the juice of one lemon into the dish. Taste for salt and pepper. When the seasoning is right, layer the thin lemon slices over the pan and scatter half of the crumbled goat cheese over the top.
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Serve garnished with more crumbled goat cheese and chopped parsley.
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Scatter the dish with lemon slices before serving.