2 hours, plus soaking time for the mushrooms and cooling time for the lasagna. Serves 12
1 2/3 cups unbleached flour, plus extra for rolling the dough
1. Place the flour in the bowl of a mixer or food processor. Add the eggs and mix until a dough starts to come together. The dough should feel like soft clay; if it feels moist, add a little more flour. Turn it out onto a well-floured work surface and knead until it forms a cohesive dough, 4 to 6 turns. Wrap the dough in plastic wrap and refrigerate it to give it time to relax, at least an hour. You'll know it's ready when you poke an indentation with your fingertip and the dough does not spring back.
2. Line the counter with kitchen towels. Divide the dough into 4 pieces. Take one piece (leaving the others under plastic wrap), flatten it slightly, flour it lightly and pass the dough through a pasta machine with the rollers adjusted to the widest setting. Fold in overlapping thirds as you would a letter and pass through again. Repeat until the dough feels silky smooth, 3 or 4 more turns.
3. Now start thinning the dough: Crank the machine two stops tighter and pass the dough through. Repeat, cranking the machine ever tighter until the sheet is thin enough that you can see your hand through it when held up to the light. This will be about setting No. 6. If the dough feels too moist, dust with a little more flour to keep it from sticking. Cut the finished dough sheet into roughly 12-inch lengths and arrange on the kitchen towels. Don't let the cut sheets touch, as they may still be slightly sticky.
4. Repeat, kneading, rolling and cutting all the pasta dough.
5. Cook the pasta, 4 to 6 sheets at a time, in a large pot of generously salted boiling water. The pasta will be done when it floats to the surface, in less than 30 seconds.
6. Gently remove the pasta from the boiling water with a skimmer and transfer it to a large work bowl filled with cool water to stop the cooking. Carefully rinse each sheet under running water, then rub it with your fingers to remove any excess water. Spread it flat on a kitchen towel to dry until you're ready to assemble the lasagna.
2 ounces dried porcini mushrooms
3 tablespoons oil
1/4 cup (½ stick) plus 3 tablespoons butter, divided, plus more for greasing
1/3 cup finely chopped onion
1/3 cup chopped, peeled and seeded tomatoes
2 tablespoons chopped parsley
1 1/2 pounds button or cremini mushrooms, sliced approximately ¼-inch thick
Freshly ground black pepper