In a medium bowl, add eggs, yolks, pepper, cheese and whisk until smooth.
Bring 3 quarts of water to a boil and add a generous amount of salt (about 1 tablespoon). Add pasta and cook according to the package instructions. During the last minute or two of cooking time, add the peas. Reserve about 1 cup pasta water, then drain the pasta and transfer it back to the pot.
While whisking the egg mixture constantly, slowly pour in ½ cup of the hot reserved pasta water. With the pot over low heat, pour the egg mixture over the pasta along with the butter and toss/stir immediately to coat the pasta for 3-5 minutes, or until the liquid has reduced into a silky sauce. You want to stir pretty constantly (arm workout!). Stir in the arugula until wilted.
Serve topped with lots more cheese and black pepper. Zest lemon over top, if using.