Bring a large pot of water to a boil for the pasta.

Slice the cabbage into quarters, then slice out the core. Use a mandoline or sharp knife to thinly slice or shred the cabbage to get about 10 cups of cabbage.

Heat a 12-inch sauté pan over medium-high with 3 tablespoons of the olive oil. Once shimmering, add the cabbage, 1 teaspoon kosher salt and lots of black pepper. Use tongs to coat the cabbage in the oil. Cook for 10 minutes, stirring just occasionally, until tender, silky and starting to brown in spots. If the cabbage browns too quickly, deglaze with a splash of water and lower the heat to medium.

Add the garlic, thyme and crushed red pepper, and stir frequently for 2 minutes, or until aromatic and garlic is just turning color. Remove from the heat and set aside.

Once the water is boiling, salt it generously (2 to 3 tablespoons kosher salt). Add the pasta and cook for the minimum time the package instructs, until barely al dente. Scoop out a ladle of pasta water, then drain the pasta and return to its pot.

While the pasta cooks, make the sauce: In a measuring cup, whisk together the milk, nutritional yeast, ½ teaspoon kosher salt and remaining 2 tablespoons olive oil.

Add the sauce and crushed walnuts to the pasta. Over medium-high heat, toss well with tongs until the pasta is well-coated in the sauce and is al dente, 1 to 2 minutes. If needed, add a splash of pasta water to help the sauce cling to the pasta. Fold in the cabbage.

Remove from the heat and stir in the lemon juice and a generous amount of black pepper. Serve in bowls and garnish with the basil and a pinch of flaky sea salt. Refrigerate leftovers for 3 to 5 days.