Cook the chicken: In a large skillet, melt the butter and add the olive oil over medium-high heat. Add the chicken pieces, season with salt, black pepper, and paprika, and cook until the chicken is golden brown and cooked through, about 5-6 minutes.

Sauté the aromatics: In the same skillet, add the chopped onion and minced garlic. Cook for 2 to 3 minutes, stirring, until the onion becomes clear and releases its aromatic scent.

Add the carrots and orzo: Stir in the matchstick carrots and orzo pasta. Cook for 1-2 minutes, allowing the orzo to lightly toast in the butter and oil mixture.

Add the broth and cook: Pour in the chicken broth, stirring well. Bring the mixture to a simmer, then cover and cook for 8-10 minutes, or until the orzo is tender and most of the liquid has been absorbed.

Add the broccoli and cream: Add the chopped broccoli and heavy cream to the skillet. Stir well, cover again, and cook for an additional 3-4 minutes until the broccoli is tender.

Stir in the cheese: Remove the skillet from heat and stir in 1 ¼ cup of the sharp cheddar cheese, mixing until it melts and creates a creamy sauce.

Add the chicken and final garnish: Return the cooked chicken to the skillet, stirring until well combined. Sprinkle the remaining ¼ cup of cheddar cheese on top, cover for a minute to allow the cheese to melt, then serve hot.