Bring a large pot of salted water to a boil. Cook the pasta according to package directions until al dente. About 2 minutes before the pasta is done, add the broccoli florets to the boiling water to blanch them.
While the pasta cooks, heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Season the chicken with salt and pepper, then add it to the skillet. Cook until golden brown and cooked through, about 6–7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the remaining 1 tablespoon of olive oil. Add the minced garlic, oregano, and red pepper flakes (if using). Sauté for about 30 seconds until fragrant.
Pour in the heavy cream and bring to a gentle simmer. Stir in the Parmesan cheese until melted and the sauce is smooth. Return the cooked chicken to the skillet and stir to combine.
Drain the pasta and broccoli, reserving about 1/2 cup of the pasta cooking water. Add the pasta and broccoli to the skillet with the sauce. Toss everything together, adding a splash of reserved pasta water if needed to loosen the sauce.
Remove from heat and stir in the lemon juice. Taste and adjust seasoning with salt and pepper. Garnish with fresh parsley and extra Parmesan before serving.
Notes
Garnish with fresh parsley and extra Parmesan before serving.