Fill a large pot with water and set it to boil.
Heat a large skillet on medium to medium-high heat and add 2 tbsp of olive oil. While it heats, sprinkle the chopped chicken with salt and pepper to taste. Saute the chicken, letting sit in the pan for at least 1-2 minutes so it browns. Gently loosen the chicken cubes and flip, letting the other side brown. Cook for about 6-8 minutes total. To check for doneness, cut a large cube in half. Remove chicken from heat and set aside in a bowl. Cover to keep warm.
Add noodles to the boiling water and cook according to the package instructions. Drain.
Meanwhile, add the remaining olive oil to the skillet and saute leeks over medium until browned. They will not require a lot of stirring, which leaves you free to make the bechamel/white sauce. Add the frozen peas just 3-4 minutes before you are ready to serve so they are warmed through but not browned.
In a small pot, melt butter over medium heat. Gradually whisk in flour, salt and pepper until the mixture is smooth. Whisk in milk a little at a time and add salt and pepper to taste. Simmer for 1-2 minutes until thickened. OPTIONAL: Add in the grated parmigiano reggiano cheese for a a cheesier sauce. If you add the cheese, I recommend leaving out the salt until this stage and adjust to taste.
Place noodles in bowls and top with the chicken cubes. Spoon bechamel sauce over chicken and noodles. Top with the leek and pea mixture. Enjoy!