Rigatoni with Lemon-Chile Pesto and Grated Egg
['12 ounces rigatoni or other short pasta', 'Kosher salt', '4 hard-boiled large egg yolks', '8 tablespoons unsalted butter, divided', '1 teaspoon finely grated lemon zest', '2 tablespoons fresh lemon juice', '1 teaspoon finely grated Meyer lemon zest', '2 tablespoons fresh Meyer lemon juice', '1/2 teaspoon crushed red pepper flakes', 'Freshly ground black pepper', '1/2 ounce Pecorino', 'finely grated (about 1/2 cup)']
Cook pasta in a large pot of boiling salted water, stirring occasionally, until very al dente (pasta will still be opaque and very firm in the center). Drain pasta, reserving 1 1/2 cups pasta cooking liquid.
Meanwhile, finely grate egg yolks on the small holes of a box grater and set aside.
Heat 6 tablespoons butter in a large skillet over medium-high. Add both kinds of lemon zest and juice and red pepper flakes, swirling pan to incorporate. Add pasta and 1 cup pasta cooking liquid and cook, tossing often and adding more cooking liquid to help finish cooking pasta, until pasta is al dente and sauce is thickened and coats pasta, about 5 minutes. Taste and season with salt and pepper.
Add Pecorino and remaining 2 tablespoons butter to pasta and toss until melted. Serve pasta topped with reserved grated egg yolks.
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