Heat oven to 400°F. In 12-inch skillet, heat oil over medium heat. Add onions; cook 8 to 10 minutes, stirring frequently, until lightly browned. Add sage, garlic, salt and pepper; cook 2 minutes. Add squash and broth. Heat to simmering; reduce heat to medium-low. Cover and cook 12 to 14 minutes or until squash is tender. Remove from heat; mash mixture with potato masher until only slightly lumpy. Stir in ⅓ cup of the hazelnuts.

Meanwhile, in 3-quart heavy saucepan, melt butter over medium heat. Beat in flour with whisk; cook and beat 2 minutes. Slowly beat in milk. Increase heat to medium-high; add salt. Heat to boiling, beating constantly. Reduce heat; simmer 4 to 6 minutes, beating occasionally, until thickened. Remove from heat; stir in ½ cup of the Parmesan cheese.

To assemble: Spray 13x9-inch (3-quart) glass baking dish with cooking spray. In medium bowl, mix fontina cheese and remaining ½ cup Parmesan cheese. Reserve 1 cup of the cheese mixture for topping. Spoon ¾ cup of the sauce into bottom of baking dish. Top with 3 of the lasagna noodles in single layer. Evenly top with ¾ cup of the sauce and 1 ⅓ cups of the butternut squash filling. Sprinkle with one-third of the cheese. Repeat layers twice. For final layer, top with 3 noodles; pour remaining sauce over top, and sprinkle with reserved 1 cup cheese mixture. Cover with foil; bake 30 minutes. Remove foil; top with remaining ⅓ cup toasted hazelnuts. Bake, uncovered, 9 to 11 minutes or until bubbly and lightly browned. Let rest 15 minutes before cutting.

To freeze: Line 13x9-inch (3-quart) glass baking dish with plastic wrap, leaving enough overhang to completely enclose assembled lasagna. Cool filling and sauce completely, covered, 30 to 40 minutes in refrigerator before assembling lasagna. Assemble lasagna in dish; cover with another layer of plastic wrap. Freeze unbaked lasagna about 8 hours or until completely frozen. Transfer frozen lasagna to labeled 2-gallon resealable freezer plastic bag. Place remaining ⅓ cup hazelnuts in 1-quart resealable freezer plastic bag, and store in same freezer bag with lasagna. Remove air; seal and freeze up to three months. To bake: Remove plastic wrap, and transfer to 13x9-inch (3-quart) glass baking dish sprayed with cooking spray. Cover tightly with foil; thaw in refrigerator until completely thawed, up to 48 hours. Heat oven to 400°F. Bake 55 minutes; remove foil. Top with remaining ⅓ cup toasted hazelnuts. Bake 15 to 18 minutes or until bubbly and lightly browned (165°F in center). Let stand 15 minutes before cutting.