Start by seasoning both sides of the chicken breasts generously with salt and freshly ground black pepper to enhance their flavor.
In a large skillet, heat the olive oil and butter together over medium heat. Once the oil is shimmering and the butter has melted completely, add the seasoned chicken breasts to the skillet. Sear each breast until they are golden brown and cooked through, about 5-7 minutes per side. Once cooked, remove the chicken from the skillet and set aside on a plate.
In the same skillet, without washing, add the sliced mushrooms. Sauté them for around 3-4 minutes, stirring occasionally, until they are tender and have released their moisture.
Next, add the minced garlic to the mushrooms and continue to sauté for about 1 minute, or until the garlic is fragrant and just beginning to brown.
Carefully pour in the balsamic vinegar, using a wooden spoon to scrape up any browned bits from the bottom of the skillet; this will add depth to the sauce. Allow the mixture to simmer for about 1-2 minutes to reduce slightly.
Reduce the heat to low, then stir in the heavy cream. Mix thoroughly until the cream is fully combined, creating a rich and creamy sauce.
Return the seared chicken breasts to the skillet, ensuring they are well-coated in the luscious mushroom cream sauce. Allow the chicken to simmer gently in the sauce for another 5-7 minutes, or until the chicken reaches an internal temperature of 165°F and is fully cooked through.
Taste the sauce and adjust the seasoning with extra salt and pepper if needed to suit your preference.
Just before serving, garnish with freshly chopped parsley to add a touch of color and freshness to the dish.
Notes
For an impressive presentation, serve over mashed potatoes or pasta.