Season both sides of the chicken breasts with salt and pepper. Heat olive oil in a large skillet over medium heat. Add the chicken to the pan and cook for about 5 to 6 minutes on each side until golden brown and fully cooked. (Tip: The internal temperature should reach 165°F). Remove the chicken from the skillet and set it aside on a plate while keeping it warm.
Using the same skillet, melt the butter over medium heat. Add minced garlic and sauté for about 1 minute until fragrant. Toss in the sliced mushrooms and cook, stirring occasionally, for 3 to 5 minutes. They should turn golden and tender.
Pour the chicken broth into the skillet, scraping any browned bits from the bottom (adds flavor!). Stir in the heavy cream, dried thyme, and Parmesan cheese. Allow the sauce to simmer for 5 to 7 minutes until it thickens slightly.
Return the cooked chicken to the skillet, spooning the garlic mushroom sauce over each piece. Lower the heat and simmer for an additional 2 to 3 minutes to reheat the chicken and blend the flavors.