Pat the chicken with a paper towel to remove excess moisture and season with salt and pepper.
Heat 1 tablespoon of oil in a cast iron skillet over medium-high heat. Add chicken, smooth-side down, and sear for 13 minutes. Don’t move the chicken around while it cooks, as it will disrupt the sear and may cause the chicken to stick to the pan. Instead, rotate the pan to move the oil around to help loosen the chicken from the pan. Use a thin spatula and carefully lift the chicken and transfer to a plate.
Reduce the heat to medium if oil begins to splatter.
Preheat the oven to 180C. Add the butter and mushrooms to the pan and cook until they begin to brown and caramelize, about 8 minutes.
Add the white wine and use the metal spatula to scrape up the chicken remnants. This will give the sauce excellent flavor.
Add the garlic and lemon juice and cook for 1 minute. Add the whipping cream. Add the chicken , sear-side up, and heat for 5 additional minutes.
Transfer the pan to the oven and bake for 15 minutes.
Serve with brown rice and roasted green beans.