Spring Green Spaghetti Carbonara

Name: Spring Green Spaghetti Carbonara
Ingredients: Kosher salt and freshly ground black pepper; 12 ounces spaghetti, such as De Cecco; 1/2 pound snow peas, julienned lengthwise; 1 cup shelled fresh peas (1 pound in the pod), or frozen peas; 12 to 14 thin asparagus, bottom third discarded and tips sliced in 2-inch pieces; 2 tablespoons good olive oil; 8 ounces small-diced pancetta; 1/2 cup heavy cream; 2 extra-large eggs; 2 extra-large egg yolks; 3/4 cup freshly grated Italian Parmesan cheese, plus extra for serving; 5 scallions, white and green parts, thinly sliced diagonally; 1/4 cup minced fresh chives, plus extra for serving; Zest and juice of 1 lemon