How to Make It
Preheat the oven to 350°. In a small, heatproof bowl, cover the morels with the boiling water. Let stand for about 20 minutes, until softened. Lift the morels from the water and rinse well. Let the soaking liquid stand so the grit settles to the bottom of the bowl.
In a very large, deep skillet, melt the butter in the oil. Add the leeks and the 1/2 teaspoon of paprika, cover and cook over moderate heat, stirring, until softened, about 5 minutes. Add the Riesling and simmer until reduced to 1/3 cup, about 4 minutes. Add the stock and slowly pour in the mushroom soaking liquid, stopping before you reach the grit. Add the morels and a pinch of salt.
Season the hens with salt, pepper and paprika. Set them on top of the leeks and morels, breast sides up, cavities facing outward. Roast in the upper third of the oven for about 1 hour, until the juices in the cavities run clear and an instant-read thermometer inserted in the inner thighs registers 160.
Transfer the hens to a carving board and let rest for 10 minutes. Simmer the pan juices over moderate heat until the liquid is reduced to 1/2 cup, 6 minutes. Add the lemon zest and juice and remove from the heat. Stir in the tarragon; season with salt and pepper.
Transfer the hens to plates and serve with the leeks, morels and sauce.