, plus more for optional garnish
, finely chopped
COOK tagliatelle in a large pot of boiling water, following package directions but omitting salt, until tender, 10 to 11 min. Drain pasta, reserving 1/4 cup of cooking water.
WHISK egg with egg yolk, grated parmesan, cream and 1/2 tsp salt in a medium bowl. Generously season with fresh pepper. Set aside.
HEAT a large non-stick frying pan over medium. Add chorizo and cook until lightly golden, 3 to 5 min. Stir in pasta. Remove from heat. Stir egg mixture then add, stirring quickly, coating the pasta. Stir just until the egg mixture begins to thicken. Stir in enough pasta water to make the sauce creamy. Season with more fresh pepper. Sprinkle with shaved parmesan, if desired.
WHISK oil with vinegar and 1/4 tsp salt in a large bowl until combined. Add arugula and toss until coated. Serve with pasta.