Prep the chicken and produce: Pat the chicken breasts dry and season both sides generously with salt, pepper and 1/2 tsp Italian seasoning. Drying the chicken removes surface moisture so it browns instead of steams. Peel and finely dice the onion and mince the garlic; set aside.

Bring a large pot of salted water to a rolling boil for the pasta. Cook the pasta 1–2 minutes shy of package directions for al dente—the pasta will finish cooking in the sauce and you want some bite left so it doesn't go mushy.

Heat a large, heavy-bottomed skillet (10–12-inch) over medium-high heat. Add 1 tbsp olive oil and 1 tbsp butter. When the fat shimmers and the butter stops foaming, add the chicken. Sear 4–5 minutes per side (depending on thickness) until deeply golden and a thin band of white appears 3/4 of the way up—this caramelized crust creates Maillard flavors that make the sauce taste richer. Transfer chicken to a cutting board and tent with foil to rest (carryover heat will finish cooking).

Lower heat to medium and add the remaining 1 tbsp butter to the skillet. Add the diced onion and a pinch of salt; sweat the onion 4–5 minutes until soft and translucent—this builds the sweet, savory base for the sauce. Add the minced garlic and 1/4 tsp crushed red pepper flakes; cook 30–45 seconds until fragrant. Garlic cooks quickly—browning it will cause bitterness, so keep the heat moderate.

Make a light roux to thicken the sauce: Sprinkle 1 tbsp flour over the softened onion-garlic and stir for 60 seconds to cook the raw flour taste and let it bind the fat. This creates a stable base so the cream won't separate.

Deglaze with chicken broth, scraping up browned bits from the pan—those fond pieces are concentrated flavor. Add the broth and stir, letting it reduce about 2 minutes until slightly thickened. Reduce the heat to medium-low before adding cream to avoid violent simmering.

Add the heavy cream and bring to a gentle simmer (small bubbles at the edge). Simmer 3–5 minutes until the sauce coats the back of a spoon and begins to thicken. Simmering reduces water and concentrates flavor; gentle heat prevents the cream from breaking.

Stir in the grated Parmesan in two additions, stirring and off-heat between additions so it melts smoothly into the sauce. Parmesan both thickens by melting into the cream and adds umami-salt intensity—tasting and seasoning here is essential. Add lemon juice and remaining 1/2 tsp Italian seasoning; these brighten and balance the richness.

Slice the rested chicken into 1/3-inch slices against the grain so it stays tender. Return the cut chicken to the sauce to warm through for a minute. Returning the chicken also allows it to pick up sauce flavor.

Drain the pasta, reserving 1 cup of the pasta cooking water. Add the drained pasta directly into the skillet with the sauce and toss to combine over low heat. Add pasta water a few tablespoons at a time as needed—the starchy water helps the sauce cling and reach a silky consistency (this is called 'mantecatura' in Italian cooking). If the sauce is too thick, add more reserved water; if too thin, simmer a minute to reduce.

Taste and adjust seasoning with salt, pepper and a final squeeze of lemon if desired. Serve immediately topped with a sprinkle of chopped fresh parsley and extra grated Parmesan.

Leftovers & storage: Cool quickly and refrigerate up to 3 days in an airtight container. Reheat gently in a skillet with a splash of broth or water to revive the sauce—avoid microwave reheating at high power which can break the cream emulsion.