slice all the squash and zucchini on a mandolin about 1/4 inch thick.
split all the asparagus, you can crush or split, but break the outer skin to soften.
season everything lightly with salt and pepper.
on a roasting tray with a rack, roast all of these vegetables primarily to reduce the liquid in them roast for between 15 to 20 minutes, until they just slightly brown.
boil the cauliflower in the stock with 50/50 stock to water, enough to cover the broken up cauliflower until fork tender.
put all of the cauliflower in a blender and blend until smooth, adding 1/2 the butter, and all of the milk and half and half. Put about 1/2 cup of the stock in the blender as well.
brown the ground chicken and set aside, seasoning lightly with salt and pepper. Put a splash of the chicken stock in with the chicken to add flavor as it browns.
press the extra moisture from the squash and zucchini when it is done in the oven.
Place the remaining butter into the same pan you browned the chicken in and sauté the mushrooms just slightly. They should still remain firm if you bit into one, not soggy or soft. Just barely cooked, mostly to get the butter on, and a hint of the moisture out.
Add about 1/2 of the cauliflower cream sauce to the mushrooms and toss. Simmer it for another 5 minutes or so.
Take 2 eggs, scramble them and add to the remaining sauce in the blender. Blend it for a few seconds to incorporate the egg into the mixture.
using a strainer, remove the mushrooms from the sauce, saving this sauce for another dish. There will undoubtedly be too much sauce for this dish before you are done, and the remaining simmered sauce will be a pleasant soup if you reserve it. Be sure NOT to consume the raw egg mixture as soup, that is intended to help set up the lasagna.
put some of the egg mixture onto the bottom of a lasagna dish.
cover that with one layer of squash.
put the mushroom mixture over the squash, and add a tiny bit of the egg sauce if needed, depending on how dry it is.
put the meat over the mushrooms.
put down one more layer of squash.
add the remaining egg mixture, it should be very thick by now, so don’t spread it thin, it should be about the same thickness as the mushroom layer.
Final layer of squash.
sweat the broccoli slaw in the same pan once it is empty, but don’t clean the bits or left over sauce before adding the slaw. Get it pretty dry if you can.
Add the olive oil to this mixture, and continue cooking until it gets just a bit crispy.
layer the slaw on top of that last layer of squash. There should be no sauce on top of the squash, it should remain dry. This will create a platform for the slaw to crisp up in the oven.
if there is any liquid forming in the pan, use a baster to suction it out before putting it in the oven.
bake at 400 for about 40 to 45 minutes, until the slaw is crispy and browning on top.
Remove it from the oven, and drain off as much liquid as you can.
add a sprinkle more of parmesean cheese to the top and return to the oven for 5 more minutes.
Final draining of liquid if needed.
Let it rest for a few minutes, then slice with a sharp knife and serve.