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In a bowl, mix the eggs, Parmesan, cream, salt, and pepper. Add lemon zest and set aside.
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Cook peas for 3 minutes in a large saucepan of boiling, salted water. Use a slotted spoon to remove them, cool, and set aside.
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Cook pasta according to package instructions in the boiling, salted cooking water used for the peas.
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Meanwhile, season the chicken cubes. Heat olive oil in a skillet over medium heat and brown chicken for about 5 minutes on all sides.
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Drain pasta and reserve 60 mL (¼ cup) of cooking liquid.
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Return pasta to saucepan, add peas, chicken cubes, cream-Parmesan mixture, and reserved cooking water if necessary to thin the sauce.
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Stir, taste, and adjust seasoning, as needed.
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Serve in bowls topped with parsley and bacon if you like.
TIP
For a spicier version, add a little Espelette pepper or other hot pepper.
NO WASTE
After zesting the lemon, reserve the juice to use in a salad or as a replacement for vinegar.