Place a skillet over medium heat. Add one tablespoon each of butter and vegetable oil. Once the butter is melted, add the chicken. Cook for 8 minutes, stirring occasionally, until the chicken is cooked through. Transfer the chicken to a bowl and set aside.
Add the final tablespoon of vegetable oil to the skillet. Add the carrots to the skillet. Cook for about 3-4 minutes. Stir in the garlic and cook for another minute.
Stir in the orzo and cook for another minute or so to toast the orzo slightly.
Pour in the chicken broth and stir. Cover and cook, stirring occasionally for about 6 minutes. Stir in the broccoli. Continue cooking uncovered for another 3 minutes or until the pasta is cooked though and the vegetables are tender.
Stir the cooked chicken back in along with any juices that have accumulated.
Add the remaining butter, the lemon zest and lemon juice. Stir to combine.
Add ¾ of the feta cheese and stir to combine.
Season with salt and pepper as needed.
