Preheat the oven to 350° F.
Combine the flour (I use about ½ cup), salt and pepper in a bowl or plastic bag. Add the chicken pieces and mix or shake until coated. Tap off the excess flour.
In a large oven-proof skillet or shallow flameproof casserole, melt the butter with the oil. Add the chicken pieces and cook over high heat, turning occasionally, until deeply browned and crusty 10 to 12 minutes. Transfer the chicken to a large plate.
To the same skillet or casserole, add the onion and mushrooms and cook over low heat until softened, 5 minutes.
Add the wine and cook over high heat until reduced by half, about 5 minutes.
Add the bay leaf, a few thyme sprigs, artichokes and stock and bring to a boil. Return the chicken to the pan. Transfer to the oven and braise until the meat is tender, 45 minutes or so.
Return the skillet or casserole to the stove, over high heat, and stir in the dairy (cream, half and half or sour cream).
Bring to a boil for about 5 minutes, allowing the sauce to thicken.
Remove the bay leaf and what’s left of the sprigs before serving.