In a 10- to 12-inch frying pan over high heat, frequently stir onions with 2 tablespoons butter until limp, about 5 minutes. Scoop out 1/2 cup of the onion mixture and set aside. To frying pan, add ginger, curry powder, and squash; mix, then scrape into a bowl. Stir ricotta cheese into squash mixture and add salt to taste. Add egg and mix well.
Rinse and dry frying pan; return to high heat. Add remaining butter, the reserved onion mixture, and flour. Stir until flour is golden, about 3 minutes. Remove from heat; add broth and half-and-half. Mix until smooth. Stir over high heat until mixture boils; reduce heat and simmer, stirring often, about 5 minutes. Add 1/2 teaspoon nutmeg and salt to taste.
Meanwhile, in a 5- to 6-quart pan over high heat, bring about 3 quarts water to a boil. Add lasagna and cook, stirring occasionally, until tender to bite, 12 to 16 minutes. Drain, immerse in cold water, then drain again.
Spread about 1/2 cup of the onion sauce evenly over the bottom of a 9- by 13-inch casserole. Arrange 1/2 the lasagna neatly over sauce to cover. Spoon all the squash mixture onto pasta and spread level. Cover neatly with remaining pasta and coat completely with remaining onion sauce. Sprinkle with parmesan cheese and dust with more nutmeg.
Bake lasagna in a 375° oven until bubbling at edges and lightly browned on top, 35 to 40 minutes. Let stand 15 to 20 minutes; cut and serve with a wide spatula.
Note: Nutritional analysis is per serving.