Aquacotta: Porcini Broth with Soft Polenta

To make the broth: Soak the porcini mushrooms in warm water to cover for 1 hour. Strain the liquid through a fine-meshed sieve and reserve; chop the mushrooms. Combine the mushroom water, chicken stock, and Marsala in a medium saucepan. Add the mushrooms to the pan and bring the broth to a boil over medium-high heat. Reduce heat and simmer for 45 minutes. Season with salt and pepper. Set aside.

To make the polenta: Bring 1-1/2 cups of the water to a boil in a medium saucepan. Add the polenta to the remaining cold water. Slowly whisk the polenta mixture into the boiling water, lower heat, and continue to cook for 20 minutes, stirring frequently. Stir in the cheese and season with salt and pepper.

To make the poached eggs: Fill an 8-inch saute pan or skillet with water. Bring the water to a boil over high heat, then reduce to a simmer. Add the vinegar and salt. Crack the eggs, one at a time, into a saucer and slide them into the simmering water. Poach for 3 to 4 minutes. Remove the cooked eggs gently from the pot with a slotted spoon. Transfer the eggs to a bowl of ice water and set aside until needed.

To serve: Preheat the oven to 350 F. Put 4 heatproof shallow soup bowls on a baking sheet. Spoon 1/2 cup polenta into each of the bowls. Press 1 slice of cheese into each serving of polenta. Bake in the preheated oven until the cheese begins to melt into the polenta, about 4 minutes. Meanwhile, reheat the broth.

Reheat the poached eggs in the hot broth for 30 seconds. Remove the eggs with a slotted spoon and place on top of the cheese. Divide the broth among the bowls and drizzle the truffle oil or olive oil over it.

Note: The broth may be made up to 3 days in advance and refrigerated, tightly covered. The polenta may be prepared and the eggs may be poached up to 3 hours in advance. Reheat the polenta over low heat, stirring constantly.