Heat the oil in a heavy large
skillet over medium-high heat. Add the squash and toss
to coat. Sprinkle with salt and pepper. Pour the water
into the skillet and then cover and simmer over medium
heat until the squash is tender, stirring occasionally,
about 20 minutes. Cool slightly and then transfer the
squash to a food processor. Add the amaretti cookies and
blend until smooth. Season the squash puree, to taste,
with more salt and pepper.
Melt the butter in a heavy medium-size saucepan over
medium heat. Add the flour and whisk for 1 minute.
Gradually whisk in the milk. Bring to a boil over
medium-high heat. Reduce the heat to medium and simmer
until the sauce thickens slightly, whisking often, about
5 minutes. Whisk in the nutmeg. Cool slightly. Transfer
half of the sauce to a blender*. Add the basil and blend
until smooth. Return the basil sauce to the sauce in the
pan and stir to blend. Season the sauce with salt and
pepper, to taste.
Position the rack in the center of the oven and
preheat to 375 degrees F.
Lightly butter a 13 by 9 by 2-inch glass baking dish.
Spread 3/4 cup of the sauce over the prepared baking
dish. Arrange 3 lasagna noodles on the bottom of the
pan. Spread 1/3 of the squash puree over the noodles.
Sprinkle with 1/2 cup of mozzarella cheese. Drizzle 1/2
cup of sauce over the noodles. Repeat layering 3 more
Tightly cover the baking dish with foil and bake the
lasagna for 40 minutes. Sprinkle the remaining
mozzarella and Parmesan cheeses over the lasagna.
Continue baking uncovered until the sauce bubbles and
the top is golden, 15 minutes longer. Let the lasagna
stand for 15 minutes before serving.
*When blending hot liquids: Remove liquid from the
heat and allow to cool for at least 5 minutes. Transfer
liquid to a blender or food processor and fill it no
more than halfway. If using a blender, release one
corner of the lid. This prevents the vacuum effect that
creates heat explosions. Place a towel over the top of
the machine, pulse a few times then process on high
speed until smooth.