
Gather all ingredients. Preheat the oven to 425 degrees F (220 degrees C).
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Whisk together flour and granulated garlic in a shallow bowl or baking dish until combined. Sprinkle chicken on both sides with salt and pepper. Working with 1 chicken breast at a time, dredge chicken in flour mixture to coat both sides, and shake off excess; set aside on a large plate.
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Heat oil and butter in a large ovenproof skillet over medium-high. Once butter is melted and shimmering, add chicken breasts to skillet, and cook until golden brown on both sides, about 8 minutes. Transfer to a clean plate. Do not wipe skillet clean.
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While chicken browns, transfer remaining flour mixture to a small bowl. Add 3 tablespoons chicken broth, and whisk until smooth to make a slurry; set aside until ready to use.
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Reduce heat under skillet to medium; add shallot, and cook, stirring constantly, until softened, about 30 seconds. Add wine, scraping up browned bits from the bottom of skillet, about 1 minute. Stir in thyme sprigs and 1 cup broth. Gradually whisk in slurry mixture until combined; bring to a simmer around edges of skillet over medium-high. Remove skillet from heat. Add browned chicken to the skillet; arrange asparagus around chicken, and immediately transfer skillet to the preheated oven.
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Bake in the preheated oven until asparagus is tender and a thermometer inserted into thickest portion of chicken registers 165 degrees F (73 degrees C), 10 to 15 minutes. Remove from the oven, and divide chicken evenly among 4 plates.
Stir crème fraîche and Parmesan into asparagus and broth mixture until fully combined. Spoon asparagus and cream sauce over chicken. Garnish with thyme leaves.
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