How to Make It
Preheat the oven to 350°. In a heatproof bowl, cover the dried porcini with the boiling water and let stand until the mushrooms are softened, about 15 minutes.
Meanwhile, in a medium saucepan, bring the chicken stock to a boil. Add the rice and simmer over moderate heat until al dente, about 10 minutes. Drain the rice; reserve the broth in a covered container in the refrigerator.
In the same saucepan, melt 3 tablespoons of the butter. Add the onion, celery and celery leaves and cook over moderate heat, stirring occasionally, until softened, about 7 minutes. Drain the porcini, reserving the soaking liquid. Coarsely chop the porcini. Add them to the saucepan and cook for 3 minutes. Remove from the heat. Pour in 1/4cup of the mushroom-soaking liquid; reserve the rest. Add the rice to the saucepan along with the cheese, season with salt and pepper and stir well.
Put the Cornish hens in a medium flameproof roasting pan. Stuff the cavities with the rice; you will have about 1 cup of stuffing left over. Wrap the remaining rice in a foil packet. Spread the 1 tablespoon of softened butter over both hens' breasts and legs and season the hens inside and out with salt and pepper.
Roast the hens in the upper third of the oven until nicely browned and an instant-read thermometer inserted in the thickest part of a thigh registers 165°, about 1 hour and 20 minutes. Transfer the hens to a platter and let rest in a warm place for 10 minutes. Increase the oven temperature to 400°. Bake the foil packet of stuffing until hot, about 10 minutes.
Meanwhile, set the roasting pan over moderately high heat. Add the wine and scrape up the browned bits from the bottom of the pan with a spoon. Add in the reserved rice-cooking broth. Pour in the reserved mushroom-soaking liquid, stopping before you reach the grit at the bottom. Simmer over moderate heat until reduced to 1 cup, 10 minutes. Season the gravy with salt and pepper and pour it into a warmed gravy boat.
Using a sharp, heavy knife, cut the hens in half and arrange on a platter, stuffing side down. Pass the gravy at the table along with the extra rice stuffing.