Prepare the vegetables: Chop the broccoli florets into small, bite-sized pieces. Dice the onion and mince the garlic cloves so they are ready for the pan.

Sauté the aromatics: Heat a large, deep skillet over medium heat. Add the olive oil and butter. Once the butter has melted and the pan is hot, add the diced onion. Sauté for 3 to 4 minutes until the onion becomes translucent. Add the minced garlic and sauté for an additional 30 seconds until fragrant.

Toast the orzo: Add the uncooked orzo pasta to the skillet. Stir and cook the orzo with the onion and garlic for about 1 minute to lightly toast the grains.

Simmer the liquid: Pour in the chicken broth and the room temperature heavy cream. Add the salt, black pepper, and cayenne pepper. Stir well to combine. Bring the mixture to a light boil, then immediately reduce the heat to medium-low. Let the orzo simmer uncovered for 5 minutes, stirring occasionally to prevent sticking.

Add the broccoli: After 5 minutes of simmering, stir the chopped broccoli florets into the skillet. Continue to cook the mixture for another 5 to 6 minutes until the orzo is tender and the broccoli has reached your desired level of softness.

Melt the cheese: Once the pasta is tender, stir in the shredded sharp cheddar cheese. Turn off the heat immediately. The residual heat from the orzo and broccoli will melt the cheese into a creamy sauce. Serve hot and enjoy!