Season the chicken breasts with salt and pepper on both sides.
In a large skillet, heat the olive oil over medium-high heat. Sear the chicken for about 4–5 minutes per side, until golden and cooked through. Remove from the pan and set aside.
In the same skillet, melt the butter. Add the sliced mushrooms and cook, stirring occasionally, until they release their liquid and start to brown, about 5–7 minutes.
Add the minced garlic and sauté for about 30 seconds until fragrant.
Pour in the chicken broth to deglaze the pan, scraping up any brown bits. Stir in the heavy cream and thyme. Let the sauce simmer for 3–4 minutes until it thickens slightly.
Return the chicken to the pan and spoon the sauce over the pieces. Simmer for another 2–3 minutes to heat through and meld the flavors.
Taste and adjust with a pinch more salt or pepper if needed. If you like a thicker sauce, let it simmer a bit longer; if you prefer lighter, loosen with a splash of broth.
Garnish with chopped parsley and serve over pasta, mashed potatoes, or a bed of rice, with the mushroom sauce spooned on top.