1/4cup freshly grated Parmigiano Reggiano cheese, plus more for shaving on top
Bring a pot of salted water to a boil.
Cut onions into halves through the roots. Place cut side down on a board. Thinly slice lengthwise.
Heat olive oil in a large skillet. Add onions and cook over high heat, stirring, until dark brown, 15 to 20 minutes.
While onions are cooking, cook pasta in boiling water according to package directions. Add peas during the last 5 minutes of cooking. Drain well, reserving 1/2 cup cooking liquid.
Add vinegar and fish sauce to onions and cook 2 minutes. Add drained pasta and peas, reserved cooking water, mint and cheese. Cook 2 minutes. Add salt and pepper. Serve in bowls. Use a vegetable peeler to shave extra Parmigiano Reggiano on top.
Adapted from Rozanne Gold’s Radically Simple: Brilliant Flavors with Breathtaking Ease (Rodale, 2010).