Pat chicken dry with paper towels, then season both sides generously with salt, pepper, garlic powder, onion powder, and Italian seasoning. Mince garlic, zest and juice the lemon, and grate the Parmesan — set each aside in small bowls.
Boil a large pot of generously salted water and cook fettuccine or linguine until al dente per package directions (8–11 minutes). Before draining, reserve at least 1/2 cup of the cloudy pasta water, then drain without rinsing and toss with a drizzle of olive oil.
Heat 1 tbsp olive oil and 1 tbsp butter in a large skillet over medium-high heat. Add chicken in a single layer (in batches if needed) and cook undisturbed for 4–5 minutes per side until golden and cooked through to 165°F (74°C). Transfer to a board, tent with foil, and rest 3 minutes before slicing.
In the same skillet over medium heat, melt remaining 1 tbsp olive oil and 2 tbsp butter, then sauté garlic for 60 seconds until fragrant. Pour in chicken broth, scraping up all browned bits from the pan, and let reduce for 2 minutes.
Reduce heat to medium-low, pour in the heavy cream, then stir in lemon zest, lemon juice, and red pepper flakes if using. Simmer gently for 3–4 minutes, stirring often, until the sauce begins to coat the back of a spoon.
Remove pan from heat (or keep on lowest setting) and stir in Parmesan in 2–3 additions, waiting until each melts fully before adding the next. Adjust seasoning with salt and pepper, and loosen with pasta water as needed for a silky consistency.
Add drained pasta to the skillet and toss with tongs to coat, adding pasta water a tablespoon at a time if needed. Nestle sliced chicken on top, warm everything through on low heat for 1–2 minutes, then plate and garnish with chopped parsley and extra Parmesan.