Pre-heat the oven to 400˚F.
Place the walnuts, ginger, garlic, lemon zest and juice, spinach, parsley and some salt and pepper in a food processor and turn the processor on. Stream about 1/3 cup EVOO into the processor to form a pesto sauce.
Drizzle the pumpkin cubes with 2 tablespoons EVOO and season with salt, pepper, paprika and nutmeg. Roast on a baking sheet for 15 minutes, then turn the cubes over and roast for 15 minutes more.
Meanwhile, bring water to boil for the pasta, salt it and cook to al dente, according to the package directions. Reserve 1 cup of the starchy water just before draining. Drain the pasta, return it to the hot pot, add the reserved water and pesto and toss to coat. Gently mix in the roasted pumpkin cubes and serve topped with lots of cheese and some pumpkin seeds, if desired.