First, use a peeler to create slices of zucchini. I experimented with a few different tools, including a mandoline, and found that a peeler worked best. You want the slices to be as thin as possible. Lay the slices of zucchini out on paper towels in a single layer, and blot them with another paper towel to soak up some of the extra moisture. Leave the slices of zucchini out to dry out a little while you prepare the bolognese sauce.
Next prepare the bolognese sauce. Melt the butter in a medium sized pot. Once the butter has melted, run the garlic cloves through a garlic press and stir them into the butter. After a minute, add the ground beef, season with salt and pepper, and use a wooden spoon to break the beef up into small pieces. Stir frequently until the beef has browned.
Pour the crushed tomatoes and tomato paste over the beef, and season with salt and pepper. Bring to a slow and steady boil and let the sauce reduce for 10 minutes.
Thaw the frozen spinach (I placed it in a fine mesh strainer and ran it under hot water) and squeeze out the excess water. Then stir the spinach and ricotta together.
To assemble the lasagna, start by pouring a thin layer of the bolognese sauce on the bottom of a casserole dish.
Then add zucchini on top. You want a nice thick layer of zucchini, I made the layer double thick.
Next add ½ of the ricotta and spinach mixture and spread it over the zucchini in an even layer.
Then add another layer of zucchini on top.
Pour half of the remaining bolognese over the zucchini.
Repeat the last steps, creating layers of zucchini, ricotta, and zucchini.
Pour the remaining sauce over the top, and sprinkle the mozzarella over.
Bake for 30 minutes at 350 degrees, and serve immediately.