Fill a large pot with 4 cups of water and 1 tbsp salt. Bring to a boil and add pasta. Cook until al dente.
While pasta cooks, combine eggs and egg yolks with 2/3 c parmesan cheese in small bowl. Season generously with salt and pepper, and set aside.
Cut bacon into 1 inch pieces and place in cold skillet. Heat over medium high heat and cook until bacon is fully cooked. Pour off grease, leaving about 1 tbsp in the hot skillet.
When pasta is done cooking, reserve 1 cup of pasta water, and drain pasta. Immediately place pasta in hot skillet with bacon and immediately pour egg and cheese mixture over pasta. Use tongs to quickly stir egg mixture into hot pasta, to cook eggs and coat pasta thoroughly. Add reserved hot cooking water as needed to thin sauce. Add peas, and remaining parmesan cheese. Serve immediately.