Preheat the oven to 375°. In a large heatproof bowl, soak the morels in the boiling water until softened, 20 minutes. Reserving the soaking liquid, rub the morels under running water to remove any grit; coarsely chop any large ones.
Season the roast with salt and pepper. In a very large ovenproof skillet, melt 2 tablespoons of the butter in the oil. Add the roast and brown over moderately high heat on 3 sides, about 4 minutes per side. Turn the roast on the fourth side and roast for about 35 minutes, or until an instant-read thermometer inserted in the center of the roast registers 125° for rare. Transfer the roast to a carving board and cover loosely with foil. Let rest for 10 minutes.
Discard any fat from the skillet and set the pan over high heat. Slowly pour in the mushroom liquid, stopping when you reach the grit. Boil the liquid, scraping up the browned bits on the bottom of the skillet, until it reduces to 1/2 cup, about 3 minutes. Strain the liquid through a fine sieve set over a bowl.
Wipe out the skillet and add the remaining 1 tablespoon of butter. Add the shallots and cook over moderate heat until softened, about 4 minutes. Stir in the morels. Add the heavy cream and the reserved mushroom liquid and simmer over moderate heat until the sauce is thickened, about 7 minutes. Season with salt and pepper. Slice the roast 1/2 inch thick and serve with the sauce.