Add olive oil to a large skillet over high heat. Add the onion and bell peppers. Season with a small pinch of salt and pepper. Sauté for 6–8 minutes, or until bright and crisp-tender. Stir in the garlic and cook for 30 seconds. Transfer everything to a plate and set aside.
Prepare the chicken cutlets according to the linked recipe above. Cook them in the same skillet, working in batches as needed so chicken does not overlap. Transfer cooked chicken to a wire rack to keep it crispy.
In the same skillet, melt the butter. Add the broth, cream, Parmesan, 1 tablespoon lemon juice, and parsley (if using). Bring to a gentle simmer over medium heat and cook for 3–5 minutes, stirring often, until thickened and smooth. Stir well to help the Parmesan fully melt into the sauce.
Meanwhile, bring a large pot of water (12 cups) to a boil. Add 1 tablespoon salt, then the pasta. Cook until just al dente according to package directions, about 4–5 minutes. Reserve 1 cup of the pasta water, then drain the pasta.
Add drained pasta and sautéed veggies to the skillet and toss to coat in the sauce. Taste and adjust with more lemon juice or salt. If needed, thin the sauce with reserved pasta water, starting with 1/4 cup. Slice or dice the chicken and arrange it on top. Finish with extra Parmesan and lemon wedges.
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Notes
Note 1: Avoid powdery, sand-like Parmesan; it doesn’t melt right and will be too salty. I grab a block of Parmesan and grate it with the small holes of a box grater for the best texture! Gently pack in the measuring cup.Storage: Best eaten right off the stovetop!