Prepare the broccoli by chopping the florets into small bite sized pieces, dice the onion and mince the garlic so everything cooks evenly

Heat a large deep skillet over medium heat and add the olive oil with the butter, when the butter is melted add the diced onion and cook until the onion becomes translucent, then add the garlic and cook briefly so it becomes fragrant without browning

Add the orzo to the skillet and stir to coat it in the oil and butter, let it warm for a short moment so it starts toasting lightly which helps it absorb flavor

Pour in the chicken broth and the room temperature heavy cream then add the salt, black pepper and cayenne, stir everything together so the liquids surround the pasta

Bring the mixture up to a gentle boil then lower the heat to medium low and let the orzo simmer uncovered while stirring occasionally to prevent sticking and to encourage even cooking until the pasta begins to swell and soften

Add the chopped broccoli to the skillet and fold it into the orzo so it cooks alongside the pasta, continue cooking until the orzo is tender and the broccoli is cooked but still has a pleasant bite

Turn off the heat and stir in the shredded sharp cheddar cheese such as Tillamook Sharp Cheddar or Cabot Sharp Cheddar so the residual heat melts the cheese into a creamy sauce, serve the dish warm and enjoy