Preheat oven to 400F. Arrange the squash on a baking sheet and lightly dress with a drizzle of EVOO, salt and pepper. Roast for 35-45 minutes, until golden at edges and tender.
Meanwhile, bring a large pot of water to a boil and under-cook pasta by about 2 minutes, a little shy of al dente.
While the water comes to a boil, heat about 2 tablespoons EVOO, a couple of turns of the pan, over medium heat in saut pan. Add garlic and stir a minute then add escarole and wilt. Season with a little salt and pepper, and add stock, simmer gently until ready to use.
In a small bowl, stir together ricotta, sage, salt, pepper and Parmigiano-Reggiano cheese.
In a saucepot, melt butter over medium heat. Whisk in flour, cook a minute or so then whisk in milk. Raise heat a bit and season sauce with salt, pepper and a little freshly grated nutmeg. Let sauce thicken to coat the back of a spoon then taste to adjust seasonings.
Drain lasagna noodles and add them back to hot pot. Stir in ricotta cheese mixture, combine evenly, then fold in roasted squash and escarole. Transfer to a casserole dish and pour the milk sauce evenly over the top. Cover with scant layer of Fontina or Gruyre cheese and place in the hot oven on center rack.
Switch oven to broil and leave casserole in oven until lasagna is brown and bubbly all over, about 4 minutes.