Brown chicken in oil, add salt and pepper. Set aside.
Melt 2/3 of the butter in the same pan; add shallots, cooking until softened. Add chopped Porcini mushrooms, wine, chicken broth, Porcini liquid, sour cream and tarragon. Stir well and bring almost to a boil. Add chicken and potatoes and simmer, covered, for about an hour. Turn the chicken and potatoes once or twice during the simmering. Remove chicken and potatoes, keep warm. Stir in the reserved butter and reduce the pan sauce until slightly thickened.
Smash the potatoes on the plate and spoon the pan sauce over the chicken and potatoes.