Bring a large pot of water to a boil. When the water is boiling, cook pasta according to package instructions. Reserve about 1 cup of the pasta water (we will use it later), then drain the cooked pasta and set aside.
Meanwhile, in a small bowl, whisk together the eggs, egg yolks, pecorino cheese, parsley, salt, and pepper.
Meanwhile, heat a large skillet over medium-high heat. Add the cubed pancetta and let cook until lightly crisp, about 6 minutes. Use a slotted spoon to transfer the crisp pancetta to a plate. Set aside.
Reduce the heat to medium and in the same skillet with the rendered fat, add the asparagus, and cook, stirring and scraping up any brown bits on the bottom of the skillet, until the asparagus is just slightly tender, about 4 minutes.
Add the green onions and garlic. Continue to cook, stirring and being careful not to burn the garlic, for another 1 to 2 minutes.
Add the peas and 1/4 cup of the reserved pasta water and cook, stirring, until the peas are tender and the water has evaporated, 3 to 4 minutes.
Add the pancetta (and any of its juices) and the drained, cooked pasta into the skillet and toss until well combined. Add 1/4 cup of pasta water at a time to rehydrate the pasta so that it is no longer dry and heat until nice and hot.
Transfer the hot pasta to the bowl with the egg mixture and continually toss until very well coated in the sauce and glossy. If for any reason your pasta sauce gets too thick, you can thin it out with a little pasta water.
Served topped with a sprinkle more of pecorino cheese, black pepper, and parsley, if desired.