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 pot and continue boiling.
When the timer goes off, use a slotted spoon to remove the broccoli and transfer it to a plate; drain the orzo in a colander and set it aside.
Meanwhile, heat a large skillet over medium heat and melt the butter.
Add the chopped or minced garlic to the melted butter and cook until fragrant and just golden, about 30 seconds to 1 minute.
Add the drained orzo to the skillet, then pour in the heavy cream (or half-and-half or milk) and add the shredded Parmesan; stir until the cheese has melted and coats the pasta.
Season with salt and pepper to taste, stir in the warm cooked chicken, then gently fold the reserved broccoli into the mixture.
Serve immediately and top with additional Parmesan if desired.