Heat the oil in a 12” skillet over medium heat until shimmering. Add the squash and cook, stirring occasionally, until spotty brown, 15 – 20 minutes.
Stir in the green onions, sage, mushrooms, nutmeg, 1/8 tsp salt, and 1/8 tsp pepper and cook until the green onions are softened, about 1 minute. Add the broth, bring to a simmer and cook, stirring occasionally, until the squash is tender, about 10 minutes.
Cook pasta according to directions. Reserve 1/2 cup of cooking water.
Add the squash mixture, parmesan and lemon juice to the pasta and toss to combine, adjusting the sauce consistency with the reserved cooking water if needed. Season with the salt and pepper to taste. Sprinkle with the almonds and serve.