Preferably use a pot with a wide and thick bottom.
Pat the chicken thighs dry and season well with salt and pepper.
Melt the butter and oil in a pot or high-sided pan. Add the chicken skin side down. If not everyone can fit, it can be done in two rounds. Add crushed garlic cloves by crushing them with the wider side of a knife. Fry the chicken until the skin is golden and crispy, or brown well if they are skinless. Turn and brown the thigh pieces on the other side as well.
Remove the chicken from the pot as long as possible. If there is a lot of fat in the pot, you can remove some of it, but leave the garlic.
Add the wine and cook until most of the liquid has evaporated. Pour in the stock and cream and bring everything to a boil. Let it simmer until the sauce has thickened a little. Stir in the tarragon and place the chicken skin side up in the sauce.
Cover the pot with a loose lid of aluminum foil and let it simmer on medium-low heat for about 15-20 minutes. Check if the meat is cooked through. Stir or shake the pot a little at regular intervals. Adjust with a little salt and pepper if necessary.
It is served, for example, with boiled rice, butter steamed asparagus beans or sugar peas and a fresh green salad.
In addition, with mushrooms
Clean 250 grams of mushrooms and divide them into even pieces. After frying the chicken, fry the mushrooms well in the pan. Pour in the white wine and continue as described.
Chicken thighs can be replaced with chicken breast. Feel free to put some herbs like tarragon and parsley under the skin. How long the chicken breasts bask in the sauce depends somewhat on the size of the breasts.