Fill a large pot with water (about 10 cups). Bring to a boil over high heat. Add pasta to boiling water, stirring occasionally, cook until al dente. Drain, reserving 1/4 cup cooking water.

In a large skillet, heat oil. Add breadcrumbs and garlic and brown for about 2 minutes. 

Remove breadcrumbs, place in a bowl and add 2 tablespoons cheese and parsley and set aside.

Whisk remaining cheese, egg yolks, egg, salt and pepper in a medium bowl. Whisk pasta water into the egg mixture slowly.

In the large pot, add kale and peas and cook 1-2 minutes over medium heat. Add drained pasta to the pot. 

Gradually add mixture to pasta, kale and peas using tongs to toss and combine. 

Plate pasta and top with breadcrumb mixture.