How to Make It
Preheat the oven to 250°. On a large rimmed baking sheet, toss the tomatoes with the parsley and 1 teaspoon of the minced garlic. Season with salt and pepper. Arrange the tomatoes skin side down on the sheet and bake for 1 1/2 to 2 hours, or until wrinkled and slightly dry. Let the tomatoes cool, then coarsely chop them.
Meanwhile, in a large skillet, heat 2 tablespoons of the olive oil. Add one-third of the mushrooms and cook over moderately high heat until golden, about 3 minutes. Stir in one-third of the remaining minced garlic, season with salt and pepper and cook for 2 minutes longer. Transfer the cooked mushrooms to a plate. Repeat twice with the remaining mushrooms and garlic, adding 2 tablespoons of oil for each batch.
In a medium skillet, heat the remaining 2 tablespoons of olive oil. Add the leeks and cook over moderately low heat until softened and golden, about 15 minutes. Add the leeks to the tomatoes and season with salt and pepper.
Melt the butter in a medium sauce-pan. Whisk in the flour and cook over moderately high heat for 3 minutes, whisking constantly. Slowly whisk in the milk and bring to a simmer over moderately low heat, whisking frequently. Continue to cook the sauce until thickened and no floury taste remains, about 5 minutes. Remove the white sauce from the heat and season with salt, pepper and the nutmeg.
Preheat the oven to 375°. In a large pot of boiling salted water, cook the lasagna noodles until al dente, 8 to 10 minutes. Drain and rinse the noodles, then toss them with a little olive oil.
In a bowl, combine the goat cheese with the ricotta and basil. Season with salt and pepper and stir in the egg.
Spread half of the white sauce in the bottom of a 9-by-13-inch glass baking dish and top with a layer of lasagna noodles. Sprinkle the noodles with half of the mushrooms and dollop half of the goat cheese mixture on top. Cover with another layer of noodles and spread with half of the remaining white sauce. Spread the tomato and leek mixture over the sauce, cover with a third layer of lasagna noodles and dollop the remaining goat cheese mixture on top. Cover with a final layer of lasagna noodles. Spread the remaining white sauce over the noodles and top with the remaining mushrooms.
Sprinkle the mozzarella over the lasagna and bake for 50 minutes to 1 hour, or until golden brown on top and bubbling. Let the lasagna stand for 10 to 15 minutes before serving.