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Step 1
Bring a large pot of salted water to a boil. Cook linguine according to package directions. Reserve ¼ cup of pasta cooking water and set aside. Drain pasta, but do not rinse.
Step 2
While pasta is cooking, heat a large cast-iron pan over medium-high heat and toast walnuts for 4 to 5 minutes, until fragrant. Remove walnuts from pan and remove pan from heat to cool. Coarsely chop walnuts and set aside.
Step 3
In the same pan over medium heat, warm 2 tablespoons olive oil. Add Brussels sprouts cut-side-down and spread out into an even layer. Cook for 4 minutes undisturbed to allow sprouts to brown. Toss and cook for another 3 minutes. Transfer Brussels sprouts to a dish and set aside.
Step 4
Lower heat to medium-low. If pan is very dry, add another drizzle of olive oil. Sauté sundried tomatoes, shallot, garlic, and thyme. Stir to combine and cook for 4 minutes, tossing occasionally and adjusting heat as necessary so garlic doesn’t burn.
Step 5
Add wine and simmer for another 4 minutes, tossing occasionally. Add nutritional yeast, lemon juice, lemon zest, and remaining 1 tablespoon olive oil. Toss to combine and cook for another 3 minutes.
Step 6
Add linguine and reserved pasta water and toss until combined. Toss walnuts and Brussels sprouts back in along with salt and black pepper. Serve immediately, garnished with vegan parmesan.