Cook the spaghetti in a large pot of boiling salted water according to the package instructions.
While the pasta is cooking, blanch the cavolo nero and garlic cloves in the same pot for 5 minutes and add in the spinach for the last minute to wilt. Use a slotted spoon to remove the greens, then drain the spaghetti and reserve the pasta water.
In a blender, combine the blanched cavolo nero, spinach, garlic, nutritional yeast, oil, vinegar, and pasta water and blend until ultra smooth. Adjust the texture of the sauce to your liking by adding more or less pasta water. Season to taste with salt.
Mix the green sauce with the cooked and drained spaghetti, adding more pasta water if needed to get the desired consistency. Then stir in the chopped sun dried tomatoes.
Heat olive oil in a small skillet and pan fry the walnuts and chestnuts for 1-2 minutes or until fragrant, then add the smoked paprika powder, tamari and maple syrup. Cook until the walnuts and chestnuts are slightly caramelized and then remove the skillet from the heat.
Serve the super green spaghetti hot, topped with the chestnuts mix and sprinkle with a little vegan parmesan to your liking.