Pat the chicken breasts dry. Season both sides with salt and pepper. In a large skillet over medium-high heat, heat 1 tablespoon olive oil until shimmering. Add chicken, skin-side down, and cook 6–7 minutes per side until golden and cooked through. Transfer to a plate and tent with foil.

Reduce heat to medium. Add remaining tablespoon of olive oil and 1 tablespoon butter. Once melted, add mushrooms and thyme. Cook, stirring occasionally, until mushrooms are golden, about 5 minutes.

Stir in garlic and cook 30 seconds until fragrant. Pour in chicken broth and scrape up any brown bits from the pan with a wooden spoon.

Remove skillet from heat and stir in remaining butter until melted and the sauce is silky. Season with additional salt and pepper if needed.

Return chicken to the pan and spoon sauce over the top. Garnish with chopped parsley and serve hot alongside rice, mashed potatoes, or crusty bread.