If the chicken breasts are very thick, pound them to an even thickness of about 1/2–3/4 inch. Pat them dry, then season both sides with the divided kosher salt and black pepper.

Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add the chicken and sear for approximately 4–5 minutes per side, until browned, then transfer it to a plate; it does not need to be fully cooked yet.

Add the remaining 1 tablespoon olive oil to the skillet. Add the sliced mushrooms and cook for 5–7 minutes, stirring occasionally, until they are browned and most of their moisture has evaporated.

Add the chopped shallot and cook for 1–2 minutes. Stir in the minced garlic and thyme, cooking for about 30 seconds, just until fragrant.

Pour in the dry white wine and scrape up the browned bits from the bottom of the skillet. Simmer for 2–3 minutes, until the wine has reduced by roughly half.

Add the chicken broth and return the chicken and any juices from the plate to the skillet. Reduce the heat to medium-low, cover loosely, and simmer for 5–8 minutes, until the thickest part of the chicken reaches 165°F.

Remove the chicken briefly or move it to one side of the skillet. Stir the butter into the sauce until melted, taste and adjust seasoning, then garnish with chopped fresh parsley before serving.