Heat the olive oil in a large skillet over medium-high heat. Add the chicken pieces, season with salt and pepper, and cook until browned on all sides (about 5 minutes). Remove chicken to a plate.
Add the onion to the skillet and sauté for 3 minutes until soft. Stir in the garlic and dry orzo, cooking for 1 minute until fragrant.
Pour in the broth and cream. Scrape the bottom of the pan to release flavor. Stir in oregano and paprika. Bring to a simmer.
Return the chicken to the pan. Cover and cook on low heat for 8 minutes, stirring occasionally.
Stir in the broccoli florets. Cover and cook for another 4-5 minutes until the pasta is tender and broccoli is cooked.
Remove from heat and stir in the shredded cheese until melted and creamy. Serve warm.
