Bring a large pot of water to a boil. Cook noodles until not quite al dente, about 2 minutes less than the package directions. Drain; return the noodles to the pot and cover with cool water.

To prepare onion filling: Meanwhile, heat 3 tablespoons oil in a large skillet over medium heat. Add onions and cook, stirring frequently, until golden brown and very soft, about 25 minutes. (If they begin to stick, add water 1/4 cup at a time to release them and prevent burning.) Add mushrooms and cook, stirring, until just beginning to soften, about 3 minutes. Add wine and 1 teaspoon salt and continue cooking until most of the liquid is absorbed, 2 to 3 minutes. Remove from heat; stir in pepper.

To prepare spinach filling: Place spinach, ricotta, basil and 1/2 teaspoon salt in a food processor and process until smooth.

To prepare white sauce: Heat 2 tablespoons oil in a medium saucepan over medium-high heat. Add flour and stir until bubbling, about 30 seconds. Gradually whisk in milk and 1/2 teaspoon salt and bring to a boil, whisking constantly. Cook, whisking, until the sauce has the consistency of thick gravy, about 1 minute. Add Gorgonzola and gently whisk until it is melted. Remove from the heat. (The sauce will continue to thicken as it sits.)

To assemble lasagna: Preheat oven to 375 degrees F. Coat a 9-by-13-inch baking pan with cooking spray.

Drain the noodles and spread out on a kitchen towel. Spread 1/2 cup white sauce in the prepared pan. Place a layer of noodles over the sauce. Spread half of the spinach filling over the noodles and top with one-third of the onion filling. Evenly spread 1/2 cup white sauce over the onions. Repeat with another layer of noodles, the remaining spinach filling, half the remaining onion filling and half the remaining white sauce. To finish, top with a third layer of noodles, spread the remaining onion filling over the noodles and then spread or dollop the remaining white sauce on top. Sprinkle with walnuts and basil.

Bake until hot and bubbling, about 30 minutes. Let rest for 5 minutes before serving.

Onions contain a volatile compound called lachrymator that reacts with the fluid in your eyes and makes them water. To chop them without crying, try wearing goggles, burning a candle nearby or cutting them under cold water. To mellow the bite of a raw onion, soak it for an hour in 1 cup cold water, 1/4 cup vinegar and 1/2 teaspoon salt and then rinse thoroughly.

The dark gills found on the underside of a portobello mushroom cap are edible, but can turn a dish an unappealing gray/black color. Remove the gills with a spoon, if desired.

Make Ahead Tip: Cover and refrigerate the caramelized onion filling (Step 2) for up to 1 day.