Slice the chicken breasts horizontally to create thinner cutlets. Season both sides with salt and pepper. Lightly coat them in flour, shaking off excess. This helps achieve a golden crust and improves sauce texture.
Heat olive oil in a large skillet over medium heat. Add the chicken and cook for about 3–4 minutes per side until lightly golden. Remove the chicken from the pan and set it aside to rest.
In the same skillet, add butter and minced garlic. Stir for about 30 seconds until fragrant but not browned. The garlic should soften and release aroma into the pan.
Pour in the chicken broth and gently scrape up the browned bits from the bottom. These bits add deep flavor to the sauce. Let the liquid simmer for 2–3 minutes to reduce slightly.
Lower the heat and stir in the heavy cream, Dijon mustard, and dried thyme. Mix well until smooth. Allow the sauce to gently simmer until it thickens slightly.
Return the chicken to the skillet and spoon sauce over each piece. Let everything simmer together for about 5 minutes. Sprinkle with fresh parsley before serving.