Bring a large pot of salted water to a boil and cook the pasta to 1 minute less than package instructions.
Beat the eggs and egg yolk in a small bowl.
In a large skillet, heat the olive oil and add the anchovy fillets. Break the anchovies up with the back of a spoon and stir until melted. Add the red pepper flakes and garlic and cook for one minute longer or until the garlic just starts to turn golden around the edges. Remove the pan from heat.
Reserving a cup of the water, drain the pasta and add it to the skillet with the anchovy sauce. Slowly add the beaten eggs to the pasta while it's still hot, tossing as you pour. Add some pasta water as needed to loosen the sauce.
Garnish with parsley and serve immediately!
Keyword anchovies, anchovy carbonara, carbonara, pantry pasta, Seafood pasta