Bring a large pot of heavily salted water ( as salty as the ocean) to a boil. Add in linguine.

While the pasta cooks, mix parmesan, egg yolks, eggs, and pepper in a medium bowl.

When the pasta has 2 minutes left, add spinach and frozen peas. Before the pasta is finished, carefully scoop out 1 cup of pasta cooking liquid with a heatproof measuring cup. Drain pasta and return it back to the pot.

Quickly whisk in ⅓ cup of the pasta liquid into the egg mixture and then add the egg mixture into pasta, tossing the pasta while you add in the egg mixture. Continue tossing the pasta until the cheese has melted and the sauce has thickened to form a glossy sauce. If the sauce is too thick, add in more pasta water 1 tablespoon at a time till you achieve your desired consistency.  

Salt and pepper to taste. It will still need more salt. Top with more parmesan and serve.