Preheat oven to 375°F.
Halve squash lengthwise then stand each half upright to trim sides and peel. Cut the bottom in half and seed. Very thinly slice the squash on box slicer or with mandolin
In a large saucepot, melt butter over medium heat, whisk in flour and bring to bubble but do not brown. Whisk in about 1 cup warm stock (reserving a little for escarole) then whisk in warm milk. Bring sauce to a low simmer and whisk occasionally while the sauce thickens and season with salt, pepper and nutmeg to taste. Season sauce, greens and squash liberally so that your lasagna does not end up bland.
In a large sauté pan, heat olive oil, 2 turns of the pan, over medium heat. Add chopped onion and garlic, and stir to soften 5-6 minutes. Wilt escarole into pan and season with salt and pepper. Add remaining 1/2 cup stock and cook greens 5 minutes to cook out the liquids and bitterness.
Toss the sliced squash with salt and pepper, and sliced sage.
Coat the bottoms of a deep dish 8×8” or 9×9” lasagna or loaf-shape pan lasagna with a layer of sauce, shingle in a layer of potatoes and season with salt and pepper. Scatter in about 1/3 of the seasoned squash and top with 1 heaping cup of the greens, season with salt, pepper and sauce. Assemble lasagna of 4 layers of potatoes, 3 layers of fillings. Top with last few cups of sauce and all of the Fontina and Parm. Arrange sage leaves on top of lasagna marking the center of where you will cut each portion when the lasagna is served.
Cover the pan and roast lasagna on the middle rack for 30 minutes. Uncover and bake 30 minutes more until very brown and bubbly. Cool to room temperature 20 minutes or so to set the lasagna then cut and serve.