Preheat oven to 425 degrees. Peel pumpkin and cut into 1-inch chunks (about 4 cups). Toss with 2 tablespoons of the olive oil, 1/2 teaspoon salt, and the honey. Roast on a baking sheet until tender, about 45 minutes.
Meanwhile, bring a pot of well-salted water to a boil. Add pasta and cook according to package directions.
While pasta is cooking, heat remaining 2 tablespoons olive oil, garlic, and anchovies (optional) in a skillet over medium-high heat until fragrant, about 1 minute. Add walnuts and pumpkin. Toss to combine and heat through. Set aside.
Drain pasta, reserving 1 cup cooking water. Toss pasta with 1/2 cup cooking water and stir in parsley and Parmesan cheese. Season with salt and pepper, and drizzle with olive oil. Transfer to a bowl, and toss well with walnut and pumpkin mixture. Serve immediately.