Step 1

To Make The Pasta: Cook the pasta in a large stockpot of generously-salted water according to package instructions.  Reserve 1/2 cup of the starchy pasta water for later, then drain the remaining water, and set the pasta aside.

Step 2

To Make The Sauce: Meanwhile, as the pasta water is heating, whisk together the eggs, milk, 1/3 cup cheese, plus a generous pinch of salt and pepper in a small bowl until smooth.  Set aside.

Step 3

To Make The Chorizo: At the same time that you add the pasta to the boiling water, add the chorizo to a large sauté pan.  Sauté over medium heat for 5-6 minutes, stirring and flipping occasionally.  Remove from heat, drain off excess grease, and leave the cooked chorizo in the pan.

Step 4

Once the pasta is drained and ready to go, transfer it immediately (you want the pasta to still be very hot!) to the sauté pan with the chorizo.  Then slowly pour the sauce mixture into the pasta, while tossing the pasta continually with a pair of tongs, until the pasta is evenly coated and the sauce is creamy and cooked.  (It's very important that you toss the pasta while the sauce is being added, otherwise the eggs can scramble.)  If you think that the sauce seems too thick, you're welcome to add in a bit of the reserved starchy pasta water until the sauce reaches your desired consistency.

Step 5

Serve immediately, garnished with extra Manchego and black pepper, if desired.