Preheat the oven to 425°. Arrange the mushrooms, stemmed sides down on a baking sheet. Brush the mushrooms with 1 teaspoon of the olive oil and season with salt and pepper. Roast for about 12 minutes, or until tender. Thinly slice the mushrooms and transfer to a plate.
Heat the remaining 2 tablespoons olive oil in a large nonreactive skillet. Season the chicken breasts on both sides with salt and pepper and add half the breasts to the skillet, skin sides down. Cook over moderately high heat, turning once, until well browned, about 5 minutes. Transfer to a plate and repeat the process with the remaining breasts. Pour off the fat from the skillet. Return all the chicken to the skillet, lower the heat to moderate, cover and cook until opaque throughout, about 5 minutes longer. Transfer the chicken to a large plate and keep warm.
Add the white wine to the skillet and boil over high heat, stirring to scrape up any browned bits, until reduced by half, about 5 minutes. Add the chicken stock and reduce by half, about 3 minutes. Add the cream and continue boiling until reduced by half, about 3 minutes. Add the cream and continue boiling until reduced by half, about 3 more minutes. Stir in the sliced mushrooms and season with salt and pepper. Set each chicken breast on a large plate, spoon the sauce over and serve with the potato and fennel hash.