Put 10 cups of water in a large pot and bring to a boil over high heat.

Meanwhile, heat oil in a large skillet over medium-high heat. Add breadcrumbs and garlic; cook, stirring frequently, until toasted, about 2 minutes. Transfer to a small bowl and stir in 2 tablespoons Parmesan and parsley. Set aside.

Whisk the remaining 6 tablespoons Parmesan, egg yolks, egg, pepper and salt in a medium bowl.

Cook pasta in the boiling water, stirring occasionally, for 1 minute. Add spinach and peas and cook until the pasta is tender, about 1 minute more. Reserve 1/4 cup of the cooking water. Drain and place in a large bowl.

Slowly whisk the reserved cooking water into the egg mixture. Gradually add the mixture to the pasta, tossing with tongs to combine. Serve topped with the reserved breadcrumb mixture.