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Heat olive oil and 1 tablespoon butter in a large skillet over medium-high heat. Pat chicken dry and season both sides with salt, pepper, and smoked paprika.
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Add chicken thighs and sear until golden, no longer pink at the center, and juices run clear, 4 to 5 minutes per side. An instant read thermometer inserted near the center should read 165 degrees F (74 degrees C). Transfer to a plate and keep warm.
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Reduce heat to medium. Add 2 tablespoons butter to the pan. Stir in shallot and cook until softened, about 1 minute. Add garlic, Dijon mustard, and thyme; cook 30 seconds more, stirring constantly.
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Carefully pour in the brandy and scrape up browned bits from the pan. Simmer until most of the alcohol is evaporated, 1 to 2 minutes.
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Add beef bone broth, chicken bone broth, and Worcestershire sauce. Simmer until slightly reduced, 6 to 8 minutes. Whisk in heavy cream and remaining 1 tablespoon butter.
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If you prefer a thicker sauce, whisk cornstarch with 1 tablespoon water to create a slurry, add to the skillet, and simmer 1 to 2 minutes more.
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Taste and adjust with salt and pepper as needed. Return chicken and any juices to the skillet, spoon sauce over, and simmer gently for 2 to 3 minutes.