Start by patting the chicken breasts dry with paper towels and seasoning them generously with salt, pepper, and the dried thyme. Heat the olive oil over medium-high heat in your skillet. Once hot, add the chicken breasts and sear each side for about 5-6 minutes until golden brown and cooked through. Remove the chicken from the skillet and set aside on a plate.
In the same skillet, add the sliced mushrooms and trimmed green beans. Sauté for 4-5 minutes until the mushrooms release their moisture and start to brown, and the green beans become tender-crisp. Stir occasionally to ensure even cooking.
Add the minced garlic to the skillet with the vegetables. Cook for about 1 minute until fragrant, being careful not to burn the garlic, as it can turn bitter quickly.
Pour in the chicken broth and stir, scraping any browned bits from the bottom of the pan. Allow the broth to reduce slightly for 2-3 minutes. Then, add the heavy cream and stir to combine. Let the sauce simmer gently until it thickens, about 4-5 minutes.
Return the chicken breasts to the skillet, nestling them into the creamy sauce with the mushrooms and green beans. Spoon some sauce over the chicken and cook for another 3-4 minutes to heat everything through and meld the flavors.
Sprinkle fresh parsley over the top for a burst of color and freshness. Serve hot, spooning extra sauce over the chicken. This dish pairs wonderfully with a side of rice, potatoes, or even the Creamy Garlic Parmesan Orzo to soak up every bit of that luscious sauce.