Slice zucchini lengthwise into 1/8" - 3/16" thick slices.  Lightly salt & pepper both sides of each slice. Let sit for a few minutes then dry slices with a paper towel.

Lightly oil a cookie sheet, or line sheet with a silicon cooking mat, and arrange zucchini slices in a single layer.

Setting oven rack so that cookie sheet will be 6 inches or so from broiler.

Broil on high for 5 minutes, remove from oven, flip slices and pat dry, then return to oven for an additional 3 minutes.

Line a cooling rack with paper towel, and place zucchini slices on it.  Repeat these steps until all slices have been broiled, and set aside.

Mix ricotta, 1/3 of the chopped spinach, and nutmeg in a medium size bowl.  You can add a little salt & pepper if you like.  Set aside.  (I intended to add an eqq to this as well but forgot - the lasagna turned out fine without it.)

In one skillet, add a couple tablespoons of olive oil, and saute the onions and shredded carrot until translucent. 

In a larger, deep skillet, heat up two tablespoons of olive oil, and 1 tablespoon of butter, and fry the chopped mushrooms along with the thyme.

When mushrooms are turning golden, clear a space in the pan and add the tomato sauce, dried basil and oregano. and stir well.

When the tomato paste starts to deepen in color, add the drained tomatoes, and the sauteed onion and carrots, and toasted walnuts.  Stir well.

The sauce is ready when most of any liquid has evaporated.  Remove from heat and set aside.

Set cooking rack to middle of the oven, and preheat to 350 degrees.

Lightly oil a 9 x 13 baking dish.

Put a very thin layer of sauce across the bottom of the dish.

Arrange one layer of zucchini slices

Spread one third of the sauce over the zucchini, followed by one third of the ricotta mixture followed by one third of the remaining chopped spinach.

Repeat the previous 2 steps.

Spread the shredded mozzarella, followed by the grated parmesan.

Arrange sliced tomatoes and fresh basil leaves over top.

Place lasagna into oven, and bake for 30 minutes, or until top starts to turn golden around edges.

Remove from oven when ready, and let cool for 15 minutes before cutting and serving.