In an oven-safe skillet, cook diced bacon until crispy over medium heat. Remove to a small bowl. Remove all but a little of the bacon fat from the pan.
Add butter and oil to the same pan and heat over medium heat. Add the chicken thighs to the pan skin side down and cook until deep golden. Flip over and brown the other side as well. Remove to a plate.
If there is a large amount of fat in the pan, remove all but a Tablespoon or so. Add the mushrooms and cook, stirring regularly, over medium-high heat, until mushrooms have cooked off their moisture and are starting to brown. Add the diced onion and cook, stirring, until onions have softened, about 2 minutes more. Add the white wine and allow to cook for about 1 minute, stirring a bit to loosen any browned bits. Add the chicken stock.
Return chicken to the pan and place in the preheated oven for 30 minutes, or until the chicken is cooked.
Remove skillet from oven and lift chicken pieces to a plate. Place skillet onto the stove-top over medium-high heat. Add the creme fraiche, cornstarch/water mixture, Dijon mustard and tarragon and cook, stirring, until sauce is hot and thickened, 2-3 minutes. Stir in reserved bacon and then return chicken to the pan. Cook a further few minutes to rewarm chicken and bacon. Serve with mashed potatoes or rice to enjoy the lovely gravy.
If you can't find creme fraiche, I would not suggest using yogurt or sour cream, as they will "break" in the wine sauce and make a slightly curdled looking sauce. Instead, use a small amount of heavy 35% whipping cream (maybe 2-3 Tbsp) - just enough to make the sauce creamy.Be sure to read the "Cook's Notes" in the original post, for more tips, options, substitutions and variations for this recipe!