Pat the chicken breasts completely dry with paper towels. Season both sides generously with salt and pepper.
Heat a large skillet over medium-high heat. Add olive oil and wait until it shimmers.
Place chicken breasts in the pan with space between each piece. Sear for 4-8 minutes on the first side without moving, until golden-brown. Flip and cook the other side until internal temperature reaches 165°F.
Transfer chicken to a plate and cover with foil to keep warm.
In the same pan (don't wash it), add mushrooms, bacon (if using), garlic, thyme sprigs, and Cajun seasoning. Cook for about 5 minutes, stirring occasionally, until mushrooms release their water and begin to caramelize on the edges.
Pour in the heavy cream. Use a wooden spoon to scrape up all the brown bits from the bottom of the pan. Stir regularly and let simmer gently for 2-3 minutes.
Add the parmesan cheese and stir until completely melted and the sauce coats the back of a spoon.
Return the chicken to the pan. Spoon sauce over the top and let everything warm together for 1-2 minutes.
Sprinkle with extra parmesan and fresh parsley if desired. Serve immediately.