Heat the olive oil in a large skillet over medium-high heat. Season the chicken breasts with salt and pepper.
Place the chicken breasts in the skillet and sear for about 5-6 minutes on each side until golden brown. Remove the chicken from the skillet and set aside.
In the same skillet, add the chopped onion and sauté for 3-4 minutes until translucent. Add the minced garlic and cook for another minute until fragrant.
Stir in the sliced mushrooms and cook for about 5-7 minutes until they are tender and browned.
Pour in the chicken broth and scrape any browned bits from the bottom of the pan. Bring it to a simmer.
Reduce the heat to low, then stir in the heavy cream, dried thyme, and dried rosemary. Return the chicken to the skillet, cover with the mushroom sauce, and simmer for another 10-15 minutes until the chicken is cooked through (internal temperature reaches 165°F).
Taste and adjust seasoning with more salt and pepper if needed.
Remove from heat and let it rest for a few minutes before serving.
Notes
Serve over creamy mashed potatoes or rice, garnished with fresh parsley.