Preheat the oven to 375°F (190°C). Lightly grease a small-to-medium casserole dish or 9×9-inch baking dish.
Bring a large pot of salted water to a boil. Cook the pasta according to the package directions until al dente.
While the pasta cooks, combine the ricotta, beaten egg, pumpkin purée, 1 cup mozzarella, Parmesan, vegetable broth, and cream in a medium mixing bowl.
Stir until the pumpkin ricotta mixture is smooth and creamy. If it seems too thick, add a small splash of additional cream or vegetable broth.
Add the minced shallot, garlic, oregano, Italian seasoning, crushed red pepper, black pepper, salt, and nutmeg. Stir until evenly combined.
Drain the cooked pasta well and immediately toss it with the baby spinach. The heat from the pasta will begin to wilt the spinach.
Add the pasta and spinach to the pumpkin ricotta mixture. Stir gently until every piece of pasta is generously coated.
Transfer the Cheesy Pumpkin Ricotta Pasta Bake mixture to the prepared casserole dish and spread it into an even layer.
Bake uncovered for approximately 15 minutes, or until the sauce is hot and beginning to bubble around the edges.
Sprinkle the remaining 1/2 cup mozzarella evenly over the top. Return to the oven for another 5–10 minutes, until the cheese is completely melted and lightly golden.
Allow the pasta bake to cool for 5–10 minutes before serving.