Heat the olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken pieces to the skillet and season with salt and pepper. Cook for 4-5 minutes until the chicken is browned on all sides but not fully cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the chopped onion and sauté for 2-3 minutes until translucent.
Add the minced garlic and cook for 30 seconds until fragrant.
Add the orzo pasta to the skillet and stir to coat it in the oil and onion mixture.
Pour in the chicken broth and water, then add the dried oregano, dried thyme, crushed red pepper flakes, and a pinch of salt and pepper. Stir to combine.
Return the browned chicken pieces to the skillet and bring the mixture to a boil.
Reduce the heat to medium-low, cover the skillet, and simmer for 10 minutes.
After 10 minutes, stir in the broccoli florets, cover again, and cook for an additional 5-7 minutes until the orzo is tender, the chicken is cooked through, and the broccoli is bright green and tender-crisp.
Remove the skillet from heat and stir in the grated Parmesan cheese and fresh lemon juice.
Adjust seasoning with additional salt and pepper if needed.
Serve immediately, garnished with extra Parmesan if desired.