Preheat the oven to 375°. Butter a deep 3- to 4-cup glass or ceramic baking dish. In a heatproof bowl, soak the morels in the boiling water until softened, about 20 minutes. Rub them to remove any grit, then lift them out and cut into 1-inch pieces. Let the soaking liquid stand for 5 minutes so the grit falls to the bottom. Pour off the liquid, leaving any grit behind, and reserve.
In a small saucepan, melt 4 tablespoons of the butter over moderate heat. Stir in the flour to make a paste, then whisk in the milk until smooth. Bring to a boil, whisking, then simmer over low heat, whisking often, until there's no floury taste, about 15 minutes. Season with salt and pepper, then scrape the white sauce into a medium bowl. Press a piece of wax paper directly on the surface of the sauce and set aside.
In a small skillet, melt the remaining 2 tablespoons of butter. Add the shallot and cook over low heat until softened but not browned, about 4 minutes. Add the morels, a pinch of salt and the reserved morel soaking liquid and simmer over moderate heat until the liquid is reduced by half, about 3 minutes. Add the cream and simmer over low heat until it is reduced by two-thirds, about 5 minutes.
Add the morel mixture to the white sauce and season with salt and pepper. Stir in the egg yolks and Parmesan until blended, then scrape the mixture into the prepared baking dish.
Set the dish in a small roasting pan and pour enough hot water into the pan to reach halfway up the side of the dish. Transfer the pan to the oven and bake the sformato for about 45 minutes, or until just set. Remove the baking dish from the pan and let stand for 5 minutes. Run a knife around the side of the dish and invert the sformato onto a serving plate. Cut into wedges and serve at once.
Make Ahead: The sformato can be prepared through Step 4 and refrigerated overnight, covered. Bake the chilled sformato for an extra 10 to 15 minutes.
Wine Recommendation: A mouth-cleansing red is a wonderful contrast to this rich custard. Try the 1994 Penfolds St. Henri Shiraz from Australia or the 1994 Beaulieu Vineyard Georges de Latour Private Reserve Cabernet Sauvignon from California.