Bring a medium pot of lightly salted water to a boil and cook the orzo according to package directions.
In the last 3 minutes of the orzo's cooking time, add the chopped broccoli to the boiling water.
When the timer ends, use a slotted spoon to remove the broccoli and transfer it to a plate; then drain the orzo and set it aside.
Meanwhile, heat a large skillet over medium heat and melt the butter.
Add the garlic to the skillet and cook until fragrant and lightly golden, about 30 seconds to 1 minute.
Add the drained orzo, the cream (or half-and-half or milk), and the shredded Parmesan to the skillet; stir to combine and melt the cheese.
Season with salt and pepper to taste, then stir in the warm cooked chicken until heated through.
Gently fold the reserved broccoli into the pasta mixture, then serve topped with additional Parmesan if desired.