Bring a large pot of water to a rolling boil and add 1 tablespoon kosher salt. Salted water seasons the pasta from the inside-out. Add the pasta and cook 1–2 minutes less than the package al dente time — it will finish cooking in the sauce and avoid a mushy result. Reserve 1 cup of pasta cooking water, then drain the pasta.

While the pasta water heats, blanch the broccoli: bring a small pot of water to a simmer, add a pinch of salt, and cook the florets 1 minute until bright green and just tender. Immediately transfer to an ice bath (or very cold water) to stop cooking and set the color. This keeps broccoli vibrant and gives a crisp‑tender texture that contrasts the creamy sauce.

Pat the chicken pieces dry with paper towels and season lightly with 1/2 teaspoon kosher salt and a few grinds of black pepper. Dry chicken sears better; moisture prevents browning.

Heat a large (12-inch) sauté pan over medium‑high heat. Add 1 tablespoon olive oil. When it shimmers, add half the chicken in a single layer and let it brown undisturbed 2–3 minutes to develop a golden crust — this Maillard browning gives deep flavor. Flip and cook another 1–2 minutes until just cooked through. Transfer to a plate and repeat with the remaining tablespoon oil and remaining chicken. Do not overcook the chicken; it will finish in the sauce and will dry out if cooked too long now.

Reduce the heat to medium and add the butter to the same pan. Once melted, add the sliced onion and a pinch of salt. Cook, stirring occasionally, 5–7 minutes until the onion is soft and translucent — slowly sweating the onion brings out natural sweetness and builds the sauce base. If the pan looks dry, add up to 1 tablespoon of the reserved pasta water.

Add the minced garlic and red pepper flakes to the softened onion and cook 30–45 seconds, stirring constantly. Garlic cooks quickly; brief cooking blooms its aroma without turning bitter.

Deglaze the pan with the chicken broth, scraping any browned bits from the bottom with a wooden spoon. Those browned bits (fond) are concentrated savory flavor. Let the broth reduce by about one-third over 3–4 minutes — concentrating the liquid intensifies flavor and helps the sauce thicken more quickly.

Lower the heat to medium‑low, then stir in the heavy cream and bring to a gentle simmer. Simmer 3–4 minutes to slightly thicken. Keeping the simmer gentle prevents the cream from separating; high heat can cause curdling.

Turn off the heat and whisk in the grated Parmesan until smooth. Parmesan both flavors and helps thicken the sauce through melting and emulsifying with the cream. Taste and adjust seasoning with salt and pepper.

To create a glossy, velvety finish, temper the egg yolk: place the yolk in a small bowl and whisk. Slowly add 1–2 tablespoons of the hot cream sauce to the yolk while whisking continuously (this raises the yolk’s temperature without cooking it). Then whisk the warmed yolk back into the pan sauce off the heat. This step adds richness and sheen without scrambling the egg.

Return the cooked chicken to the pan along with the drained pasta and blanched broccoli. Toss gently to coat everything in the sauce. If the sauce feels too thick, add reserved pasta water 1–2 tablespoons at a time until you reach a silky consistency — starchy pasta water helps bind and loosen the sauce for a perfect cling.

Finish with lemon juice and chopped parsley and adjust seasoning to taste. Lemon brightens and balances the cream’s richness while parsley adds freshness. Serve immediately with extra grated Parmesan and a crack of black pepper.