Add oil to a large nonstick skillet over medium heat. Once shimmering and hot, add onions and cook until softened (about 3-4 minutes). Add garlic and cook for 1 more minute.
Add orzo, chicken broth, milk, chicken, broccoli, salt, pepper, and red pepper flakes to the skillet and stir to combine.
Bring to a simmer. Cook over medium-high heat for 16-20 minutes, or until the orzo is cooked through (you know it is done when it is chewy but still a bit firm), and the broccoli is tender.
Add the cheese and stir until completely melted.
Garnish with parsley. Ser