Cut squash in half lengthwise. Scoop out and discard seeds. Peel onion and cut in half. Rub cut surfaces of vegetables with oil. Place squash and onion, cut sides down, in a 10- by 15-inch pan.
Bake in a 350° oven until squash and onion are tender when pressed, 40 to 45 minutes.
Meanwhile, in a 3- to 4-quart pan over medium heat, stir pine nuts until golden, about 5 minutes. Pour into a bowl.
Scoop flesh from cooked squash. Purée squash smoothly with onion in a food processor (or in a blender, a portion at a time, using some of the broth to help mix). Add puréed squash mixture to the 3- to 4-quart pan and stir in broth, half-and-half, and salt and pepper to taste.
Stir over low heat until hot, about 5 minutes; keep warm.
Meanwhile, cook linguine in 2 to 3 quarts boiling water over high heat just until the pasta is barely tender to bite, 7 to 9 minutes. Drain and pour pasta into a wide bowl.
Pour squash mixture over pasta. Dust with nutmeg and sprinkle with nuts; add cheese to taste.