Step 1Place the porcini in a bowl and pour boiling water over to cover. Let stand until very soft, about 30 minutes.
Step 2Meanwhile, combine the flour and 1 teaspoon sea salt in a mixing bowl. Whisk in the eggs and milk.
Step 3Melt 3 tablespoons butter in a 9-inch saute pan until it is bubbly and golden brown, being careful to not let it burn. Add the melted butter to the batter and whisk until very smooth.
Step 4Wipe the pan clean. Add a teaspoon of butter and heat over medium heat. Ladle in about 3 to 4 tablespoons of the batter, evenly coating the bottom of the pan. Cook until the batter is set and the bottom of the crespelle is lightly browned, 1 1/2 to 2 minutes. Flip over and cook the second side until it is golden, 30 seconds to 1 minute. Turn onto a plate. Repeat with the remaining batter to make 12 crespelles, using 1 to 2 teaspoons of additional butter as needed for the pan. Place a piece of parchment paper between each layer of crespelle to separate. Cover tightly with foil and hold in a warm oven. Wipe the saute pan clean.
Step 5Lift the porcini out of the water into a sieve. Rinse under running water to remove any grit. Line the sieve with several layers of paper towel and strain the soaking water into a large measuring cup or bowl.
Step 6Mince the porcini and combine with 1 cup of the soaking water in the saute pan. Cook over high heat until the liquid is reduced by two-thirds, about 4 to 5 minutes. Add the cream, lower the heat to medium and continue cooking, stirring occasionally, for 10 minutes. Season to taste with sea salt, set aside and keep warm.
Step 7Melt the remaining 4 tablespoons butter in a very large saute pan (or two smaller pans) over medium-high heat. Add the zucchini and cook, stirring, until all the slices are coated with butter. Season with one-half teaspoon sea salt and one-eighth teaspoon pepper. Add one-fourth cup water, cover the pan and cook 2 minutes. Remove the lid and cook until the liquid is almost evaporated. Add the prosciutto and chives, mix well and heat through. Remove from the heat.
Step 8To serve, lay 2 crespelles on each serving plate. Spoon about one-third cup zucchini mixture on one side of each. Fold in half to make half-moons. Ladle about one-fourth cup of mushroom sauce over and around the crespelles.