Preparation Steps

• Pat chicken dry and season all over with the kosher salt and black pepper. In a small bowl, whisk the flour into the cold chicken broth to make a smooth slurry; set aside. In a separate cup, stir the Dijon into the heavy cream.
• Place a large skillet over medium heat. Melt the butter and add the sliced mushrooms in an even layer with a pinch of salt. Cook undisturbed for 3 minutes to brown, then stir and continue cooking until golden and most of the moisture has evaporated, 3–4 minutes more. Transfer mushrooms and any juices to a bowl. Tip: Avoid crowding—brown mushrooms in two batches if your pan is small.
• Add the olive oil to the empty skillet and raise heat slightly to medium–medium high. Sear the chicken until lightly browned and nearly cooked through, about 4 minutes per side. Move chicken to a plate and tent loosely with foil to rest.
• Return skillet to medium heat. Add the garlic and cook just until fragrant, 20–30 seconds. Pour in the white wine and simmer, scraping up any browned bits, until reduced by about half, 60–90 seconds.
• Lower the heat to medium-low. Whisk the broth–flour slurry into the pan and simmer until it begins to thicken, 1–2 minutes. Slowly stream in the cream mixed with Dijon, whisking constantly. Stir in the thyme and let the sauce bubble gently until silky and slightly reduced, 3–4 minutes.
• Remove the pan from the heat and sprinkle in the Parmesan a little at a time, stirring until smooth. Fold the mushrooms (and their juices) back into the sauce. Taste and adjust seasoning with salt and pepper if needed.
• Slice the rested chicken across the grain or keep breasts whole. Nestle chicken into the sauce and return the skillet to low heat just until the chicken is warmed through and registers 165°F, 1–2 minutes. Finish with chopped parsley and serve hot.