Bring a large pot of salted water to a boil. Add the pasta and cook 2 minutes under al dente. Reserve ½ cup of the cooking water, then drain the pasta.
Cook onions and cabbage:
While waiting for the pasta water to boil, heat 1 tablespoon extra virgin olive oil in a large skillet over medium heat. Add the sliced onions and cook, turning occasionally, for 8 to 10 minutes, until softened. Season with salt.
Add the remaining 1 tablespoon extra virgin olive oil and the chopped cabbage. Increase the heat to medium-high and cook, turning often, until the cabbage softens and begins to char around the edges, about 6 to 8 minutes. Stir frequently to keep the onions from burning. Add a generous pinch of salt and reduce the heat to medium-low.
Finish the cabbage:
Taste and adjust the seasoning. Add the minced garlic and cook for 1 to 2 minutes, until fragrant.
Add the walnuts, brown sugar, cooked pasta, minced parsley, and a pinch of paprika. Pour in half the pasta cooking water and toss to coat. Cook for 3 to 4 minutes, until the pasta is completely cooked and glossy. Add the remaining pasta water as needed. Taste and season.
To serve:
Divide the pasta between bowls and garnish with additional parsley if you like. Enjoy!
Notes
Note 1: Start with 1 teaspoon of brown sugar and add up to 3 teaspoons if a sweeter base is wanted.