Season the chicken thighs with salt and pepper on both sides.
Have the stock or demi-glace ready. Chop the shallots and parsley.
Heat the oil and butter in a frying or sauté pan over medium-high heat.
Once the butter starts foaming, add the chicken thighs. Brown each side for about 5 minutes.
Continue cooking the chicken until thoroughly cooked, turning occasionally (about 20 to 25 minutes).
While the chicken is cooking, warm up the stock and let it reduce by half.
Mix the arrowroot with a teaspoon of water in a small bowl, then stir it into the stock to thicken slightly.
Once the chicken is cooked, transfer it to a plate and cover with foil. Keep it warm in the oven at 50 degrees Celsius.
To make the sauce, add the diced shallots to the same pan and cook over low heat for 3 to 4 minutes.
Raise the heat to high, pour the wine into the pan to deglaze, and let the liquid reduce until about 3 tablespoons remain.
Stir in the stock and let it reduce until thick enough to coat the back of a spoon.
Turn off the heat, add the butter, and incorporate it into the sauce by swirling the pan.
Place the chicken on a serving dish, add any leftover cooking juices into the sauce, and pour the sauce over the chicken. Garnish with parsley.
