Bring a large pot of salted water to a boil. Blanch broccoli for 2 to 3 minutes until bright green and crisp tender; drain and rinse under cold water. Set aside.

In the same pot, cook pasta in salted water until al dente. Reserve 1 cup pasta water, then drain pasta and set aside.

Season chicken with oregano, thyme, 1/2 tsp kosher salt, and black pepper.

Heat olive oil in a large skillet over medium high heat. Sear chicken in 2 batches until golden on the edges and just cooked through, 3 to 4 minutes per batch. Transfer to a plate.

Reduce heat to medium. Add butter to the skillet, then cook onion and garlic until translucent, 2 to 3 minutes.

Pour in chicken broth and scrape up browned bits. Simmer 1 minute.

Add heavy cream and bring to a gentle simmer over low heat. Stir in Parmesan a handful at a time until smooth.

Stir in red pepper flakes. Add a splash of reserved pasta water and stir until the sauce looks glossy and coats a spoon.

Add pasta, broccoli, and chicken back to the skillet. Toss for 1 to 2 minutes until everything is hot and evenly coated. Adjust seasoning with remaining salt if needed and loosen with more pasta water if the sauce thickens.

Serve immediately topped with parsley and extra Parmesan.