How to Make It
In a small heatproof bowl, cover the dried porcini with the boiling water and let stand until the mushrooms are softened, about 25 minutes. Drain, rinse off any grit and finely chop the porcini mushrooms; discard the soaking liquid.
In a medium skillet, heat 1 tablespoon of the butter. Add the chopped shallots and cook over moderate heat, stirring occasionally, until softened, about 4 minutes. Add the chopped porcini, season lightly with salt and black pepper and cook until fragrant, about 3 minutes. Let cool, then stir in the Gruyère cheese.
Meanwhile, in a large bowl, toss the potatoes and onion with 1 tablespoon of kosher salt and let stand for 15 minutes. Working with a handful at a time, squeeze as much of the liquid as possible from the potato-and-onion mixture into a large bowl. Transfer the squeezed potatoes and onion to a work surface. Let the liquid in the bowl stand for 5 minutes to allow the potato starch to settle on the bottom. Pour off the liquid, leaving only the starch in the bowl. Return the potatoes and onion to the bowl and toss with the starch. Season generously with black pepper.
Preheat the oven to 375°. In a 12-inch nonstick ovenproof skillet, melt the remaining 2 tablespoons of butter in 2 tablespoons of the olive oil. Remove from the heat. Add half of the potato-onion mixture, pressing it into an even layer with a spatula. Spoon the porcini-Gruyère mixture over the potatoes, leaving a 1-inch border all around the outside. Top with the remaining potato-onion mixture and press to seal the potato cake.
Cook the potato cake over moderately high heat, shaking the pan occasionally, until the bottom is golden brown, about 7 minutes. Carefully slide the potato cake onto a large, flat plate. Invert the skillet over the cake and, using oven mitts or towels, carefully invert the cake back into the skillet. Drizzle 2 tablespoons of olive oil around the edges and cook the potato cake for 5 minutes. Transfer the skillet to the oven and bake the potato cake for 30 minutes, until it is cooked through and golden on the bottom. Slide the potato cake onto a plate.
In a large bowl, whisk the remaining 1/4 cup of olive oil with the lemon juice and walnut oil. Season with salt and black pepper. Add the baby greens and tomatoes and toss again. Cut the potato cake into wedges and sprinkle them with the truffle salt, if using. Serve with the salad.