This recipe is for the ultimate garlic lover. Chicken thighs are braised until tender in a rich, roasted garlic sauce, then topped with fried garlic chips. There's even enough roasted garlic paste to whip up a loaf of garlic bread while the chicken cooks.
Cut the top third off 2 heads of garlic, exposing the tops of the garlic cloves. Put each head on a piece of aluminum foil. Drizzle each with 1 tablespoon of the olive oil and sprinkle with salt and pepper. Wrap tightly and roast until the cloves are golden brown and very soft, about 45 minutes. Let cool slightly. Leave the oven on.
Unwrap the roasted garlic and pour any garlic-flavored oil from the foil into a small bowl. Squeeze the roasted cloves into the same bowl, discarding the papery shells. Mash with a fork until smooth; set aside.
Peel and trim the remaining head of garlic. Thinly slice 5 cloves. Heat about 1/2 inch vegetable oil in a small skillet over medium heat, then add 1 slice of garlic. Cook until the garlic is at a lively sizzle, then sprinkle in the rest of the sliced garlic. Cook, stirring, until the garlic is just golden and crisp (don't overcook or it will be bitter), about 1 minute. Drain on paper towels and sprinkle with salt. Set aside.
Sprinkle the chicken generously with salt and pepper. Heat 2 tablespoons vegetable oil in a large Dutch oven over medium-high heat. Add the chicken in 2 batches skin-side down and cook, flipping once, until golden brown on both sides, about 3 minutes per side. Transfer to a plate.
Discard the oil and return the Dutch oven to medium heat. Add 2 tablespoons of butter and the remaining garlic cloves and cook until the garlic is light golden, about 3 minutes. Add the wine and use a wooden spoon to scrape up any browned bits from the bottom. Cook until the wine is reduced by half, about 3 minutes. Stir in the chicken broth, lemon juice, thyme and half of the reserved garlic paste. Bring to a boil.
Use a fork to mash together the flour and remaining 2 tablespoons butter in a small bowl until smooth. Whisk the butter-flour mixture into the Dutch oven until dissolved. Cook until thickened, about 1 minute. Nestle in the chicken skin-side up along with any collected juices from the plate. Cover and bake until the chicken is cooked through, about 25 minutes.
Meanwhile, add the Parmesan, parsley and remaining 2 tablespoons olive oil to the remaining garlic paste. Stir to combine and season with salt and pepper.
Put the bread halves on a baking sheet and spread with the garlic mixture. When the chicken has 10 minutes left, add the bread to the oven and bake until toasted, about 10 minutes.
Cut the bread into pieces. Top the chicken with the reserved garlic chips and chopped parsley.
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