Heat one tablespoon of oil in a frying pan over medium heat.
Fry the sliced leeks until they just begin to soften.
Add the pancetta and cook, stirring occasionally, until the pancetta is cooked and a bit on the crispy side. Set aside to keep warm.
Meanwhile, cook the pasta in boiling salted water according to the package directions.
Mix the lemon juice, lemon rind, Parmesan cheese, pepper and olive oil together in a small bowl.
Add a couple of tablespoons of the pasta water to the lemon mixture and mix thoroughly.
When the pasta is three minutes away from being cooked, toss in the peas. Cook with the pasta until it is done.
Set aside another tablespoon or so of the pasta water and then drain the pasta and peas thoroughly. Return to the saucepan you cooked them in.
Stir the pancetta into the pasta and peas along with the lemony cheese sauce mixture. Toss to coat all the pasta with the sauce. If it seems a little dry add another tablespoon or so of the pasta water.
Serve the pasta garnished with the chives.