Bring a large pot of salted water to a boil (make sure your water has enough salt that it tastes like the ocean).
While the pasta is cooking, heat a dry (that means no oil) 10- or 12-inch skillet over medium heat. Add the walnuts and cook, stirring, until fragrant and toasted, 4 to 5 minutes. Add the butter, swirl until melted, then add the garlic and cook, stirring, for 2 minutes. Add the cream, lemon juice, lemon zest and salt and cook, swirling, until thickened, 1 to 2 minutes. When the pasta is ready, reserve ½ cup of the pasta cooking water, drain the pasta, add the pasta to the pan and toss to coat, adding a little pasta water to loosen if necessary. Season with salt to taste.
Divide the pasta among 2 bowls and garnish with the cheese and toasted walnuts.