Preheat the oven to 425°F and line or grease a half-sheet pan for roasting the squash.

Mix the diced butternut squash with olive oil, salt, and pepper. Spread it out on the sheet pan and roast for 30 minutes, or until soft and lightly caramelized.

While the squash is roasting, melt the butter in a large saucepan over medium heat. Add the flour and whisk constantly for several minutes until it turns a pale golden color.

Gradually add the milk, whisking between each addition. Toss in the salt, pepper, nutmeg, garlic, bay leaves, and rosemary. Stir this mixture well, bringing it just to a boil. Lower to a simmer and let it thicken for about five minutes, stirring occasionally. Strain and set aside.

Preheat the oven again to 350°F and grease a 9 x 13-inch casserole pan where the roll-ups will bake.

Bring a large pot of well-salted water to a boil. Cook the lasagne noodles until al dente, then drain and reserve them for assembly.

In a wide-bottomed skillet, cook the Italian sausage and onion in olive oil until the onion is translucent and the sausage is cooked through, approximately 10 minutes. Drain on paper towels until slightly cooled.

In a large mixing bowl, combine the drained sausage and onion with the grated Asiago cheese, half of the grated Parmigiano-Reggiano, and the roasted butternut squash.

Pour about a cup of béchamel sauce onto the bottom of the greased casserole pan. Lay a cooked lasagne noodle flat on a clean surface. Spread a spoonful of béchamel on it, add some of the sausage-squash-cheese filling, and roll it up snugly. Place it in the casserole and repeat with the remaining noodles.

Pour the remaining béchamel sauce over the roll-ups and sprinkle them with the remaining Parmigiano-Reggiano and a few twists of black pepper.

Bake uncovered for about 45 minutes, or until bubbling and golden. Let the dish rest for 10 minutes, covered with foil, before serving.