How to Make It
Cook pasta according to master technique (until very al dente, about 3 minutes shorter than package directions call for).
While pasta cooks, melt 2 tablespoons butter in a large skillet over medium. Cook, stirring often, until butter smells slightly nutty and turns light golden brown, 4 to 5 minutes. Add shallot; cook, stirring often, until softened, about 2 minutes. Add sherry; cook until slightly reduced, about 20 seconds. Add stock; bring to a simmer over medium-high. Gradually whisk in 2 tablespoons butter, one piece at a time, waiting until butter is nearly melted before adding the next piece. Return to a simmer over medium-high; simmer 1 minute.
Using tongs or a spider, transfer pasta to skillet, reserving cooking liquid in pot. Increase heat under skillet to high. Gradually stir in chicken liver mousse (about 2 tablespoons at a time), alternating with cooking liquid (about 1/4 cup at a time), stirring and shaking skillet constantly, until a creamy sauce forms and coats the pasta, making sure each addition of mousse is creamy and blended before the next addition, 4 to 5 minutes total.
Remove skillet from heat; stir in cheese, rosemary, vinegar, pepper, and remaining 1 tablespoon butter until blended. Divide among 4 bowls; garnish with additional cheese and rosemary.