Heat the oil in an ovenproof skillet set over high heat. Add the chicken skin-side down and sear to a golden brown on each side. Transfer the chicken to a plate and reserve. Pour off the excess oil in the skillet.
Reduce the heat to medium-high and melt the butter in the skillet and add the mushrooms and sprinkle with salt and pepper. Cook for 4-5 minutes, stirring occasionally until the mushrooms become light brown.
Add the chopped shallot and cook until the shallot is translucent, about 1 minute. Stir in the garlic and cook until the garlic is soft and fragrant.
Add the wine and simmer for 2-3 minutes to burn off the alcohol, scraping up the bits from the bottom. Stir in the chicken broth and thyme leaves.
Place the reserved chicken thighs back into the skillet, cover with a lid and transfer to the oven. Bake for 45 minutes.
Transfer the skillet from the oven, push the chicken to the side and stir the cream into the sauce. Serve with mashed potatoes or rice.
Notes
Choose any type of mushrooms and slice them 1/4-inch thick. We used crimini, pre-slice mushrooms in this recipe.
Once the cream is added to the sauce, make sure you do not bring it to a boil or the cream will curdle.