Heat oil in a large nonstick skillet over medium-high heat until hot. Sauté mushrooms with 1/2 teaspoon salt until golden, about 8 minutes. Add vinegar and sauté until evaporated, about 1 minute. Season with salt, then transfer to a plate to cool. Serve at room temperature.
Mushrooms can be made 4 hours ahead and kept at room temperature.
Melt 2 tablespoons butter in heavy large skillet over medium-high heat. Add mushrooms and sauté until almost tender, about 5 minutes. Add garlic and sauté until mushrooms are tender and golden, about 3 minutes longer. Transfer mushroom mixture to bowl. Melt remaining 2 tablespoons butter in same skillet over medium-high heat. Add leeks and thyme and sauté until leeks are tender and beginning to brown, about 8 minutes. Add leek mixture to bowl with mushrooms. (Can be made 1 day ahead. Cover and refrigerate.)
Preheat oven to 400°F. Butter 13 x 9 x 2-inch baking dish. Whisk broth, cream, wine, 1 teaspoon salt and 1/2 teaspoon pepper in large bowl to blend. Layer 1/3 of potatoes on bottom of prepared dish. Top with half of mushroom-leek mixture, then 3/4 cup cheese. Top with half of remaining potatoes.
Pour half of cream mixture over. Top with remaining mushroom-leek mixture and 3/4 cup cheese. Cover with remaining potatoes. Pour remaining cream mixture over; sprinkle with remaining cheese.
Bake gratin uncovered until potatoes are tender and sauce bubbles thickly, about 1 hour 20 minutes. Let gratin stand 30 minutes before serving.
Special equipment: a perforated grill sheet
Whisk together juices, vinegar, and oil in a large bowl. Toss mushrooms with vinaigrette and marinate 15 minutes. Transfer mushrooms to another bowl with tongs, reserving vinaigrette.
Prepare grill for cooking. If using a charcoal grill, open vents on bottom of grill, then light charcoal. Charcoal fire is hot when you can hold your hand 5 inches above rack for 1 to 2 seconds. If using a gas grill, preheat burners on high, covered, 10 minutes, then reduce heat to moderately high.
Grill mushrooms in 3 batches on oiled grill sheet set on grill rack, with grill covered only if using gas grill, turning frequently, until golden brown, about 5 minutes per batch. Transfer to vinaigrette as grilled, then toss with sea salt.
If your sea salt is very granular and pebblelike, crush it using the flat side of a large heavy knife or the bottom of a heavy skillet. •If you’re unable to grill outdoors, mushrooms can be grilled in batches in a lightly oiled well-seasoned ridged grill pan over moderately high heat, turning frequently, about 5 minutes per batch. thickly, about 1 hour 20 minutes. Let gratin stand 30 minutes before serving.
Position 1 rack in top third and 1 rack in bottom third of oven and preheat to 450°F. Brush 2 large rimmed baking sheets with 1 tablespoon olive oil each. Place potatoes on 1 prepared sheet; drizzle 3 tablespoons olive oil over and toss to coat. Spread potatoes in single layer; sprinkle with salt and pepper. Place potatoes on top rack of oven and roast 10 minutes. Sprinkle 2 tablespoons shallots and garlic over. Transfer potatoes to bottom rack of oven and continue to roast until tender and golden brown, stirring occasionally, about 10 minutes longer. Remove from oven.
Meanwhile, toss mushrooms on second prepared baking sheet with remaining 2 tablespoons olive oil; sprinkle with salt and pepper. Spread in single layer and roast mushrooms on top rack of oven until golden brown, stirring occasionally, about 15 minutes.
Add mushrooms to potatoes; stir to combine. do ahead Can be made 2 hours ahead. Let stand at room temperature. Rewarm in 450°F oven until heated through, about 5 minutes, before continuing.
Add parsley to potato-mushroom mixture and toss; season to taste with salt and pepper and serve.
Preheat oven to 375 F (190 C)
Bring a large pot of lightly salted water to a boil. Cook lasagna noodles in boiling water for 8 to 10 minutes or as per instructions on the package. Drain the noodles and rinse with cold water
In a medium size mixing bowl, combine ricotta cheese with egg, dill, parsley and 1 teaspoon salt. Set aside
Preheat a large skillet with 2 tablespoons butter or oil. Add onions and saute over medium heat for 9-10 minutes, until translucent and golden brown. Add ¼ tsp salt and ¼ tsp black pepper when almost done. Transfer into a bowl
Using the same skillet, saute oyster mushrooms with 2 tablespoons butter or oil over high heat for 5-6 minutes
Turn heat to medium, add ½ teaspoon salt and ¼ teaspoon ground pepper, and saute for another 3 minutes
Add onions to mushrooms and continue sauteing over medium heat for another 2-3 minutes. Remove from heat and transfer to a bowl
To assemble lasagna, spread about 1 tablespoon of ricotta cheese filling on the bottom of a 8 x 8 inch baking dish. Arrange 3 noodles on the bottom of the pan (you will need to cut them to needed length).
Spread half of the ricotta cheese filing over noodles. Top with half of oyster mushroom and onion mix, followed by 1 cup mozzarella cheese and 2 tablespoons grated Parmesan cheese. Repeat another layer
Cover with foil, ensuring that foil does not touch the top of the lasagna
Bake in preheated oven for 25 minutes. Remove foil and bake additional 20 minutes
Cool for 10-15 minutes and serve