How to Make It
Preheat the oven to 425°. Put the morels in a bowl and pour the hot water over them. Place an inverted small dish over the morels to keep them submerged and let stand until softened, about 20 minutes. Lift the morels from the soaking liquid and rinse them to get rid of any grit. Chop any large morels. Reserve the soaking liquid.
In a large, deep, ovenproof skillet, heat the oil until shimmering. Season the chicken breasts with salt and pepper. Add them to the skillet, skin side down, and cook over moderately high heat until browned on the bottom, about 6 minutes. Turn the breasts and cook until browned on the bottom, about 3 minutes. Add 1 tablespoon of the butter to the skillet and swirl to melt. Put the skillet in the oven and roast the chicken for about 8 minutes, until just cooked through. Transfer the chicken to a plate and keep warm.
Melt the remaining 1 tablespoon of butter in the skillet. Add the cremini mushrooms, season with salt and pepper and cook over moderate heat until browned, about 5 minutes. Add the morels and cook, stirring, until they start to darken, about 3 minutes. Add the wine and simmer over moderately high heat until reduced to 3 tablespoons, about 3 minutes. Add the stock and slowly pour in the reserved morel soaking liquid, stopping before you reach the grit at the bottom. Simmer until reduced by two-thirds, about 6 minutes. Add the cream and tarragon and simmer until thickened, about 4 minutes. Add the lemon juice and season the sauce with salt and pepper. Add the chicken breasts to the skillet, skin side up, along with any accumulated juices, and simmer over low heat until the chicken is hot, about 3 minutes. Transfer the chicken breasts to plates and serve with the sauce.