Cut your skinless chicken thighs into 4 total pieces. Pat chicken dry with a paper towel. Season with salt and pepper and set aside.
Over medium-high heat, heat 1 tablespoon olive oil and 1 tablespoon butter in a large skillet. Once heated, add in the chicken pieces and cook until you see brown bits and the edges are golden browns. Remove them from the skillet and set them aside.
Leave the grease and juices from the chicken, add in the remaining olive oil, and heat over medium heat. Add the onion and sliced mushrooms and saute for a few minutes until the onions are translucent. Don't cook them on high heat as they can burn the onion rather than carmelize them.
Add the marsala wine and bring it to a boil and let the volume be reduced to about half.
Add the chicken broth, heavy cream, and thyme and bring to a boil again. Bring the heat down to medium-low and simmer for 10 minutes until the broth is reduced and thicken.
Add the chicken cutlets to the skillet and cover them with the sauce. Simmer for additional 1-2 minutes. Season it with salt and pepper before serving.
Warm up the cauliflower rice and serve in 4 separate places. Drop 1/2 tablespoon of butter on top and let it melt.
Serve the chicken marsala on the side of the cauliflower rice. Sprinkle chopped parsley and sprinkle some on top if desired.