Season the chicken pieces generously with salt, pepper, and dried oregano. Heat the olive oil in a large skillet or Dutch oven over medium-high heat. Add the chicken and cook until browned on all sides, about 5-7 minutes. The chicken doesn’t need to be fully cooked through yet. Remove the chicken from the pan and set it aside on a plate.
In the same pan, melt the butter over medium heat. Add the diced onion and cook for 3-4 minutes until it becomes translucent and soft. Stir in the minced garlic and cook for another minute until fragrant, being careful not to let the garlic burn.
Add the dry orzo pasta directly to the pan with the onions and garlic. Stir frequently for 2 minutes to lightly toast the pasta. This step adds a nutty depth of flavor and helps the orzo maintain its structure during the simmering process.
Pour in the chicken broth and use a wooden spoon to scrape up any browned bits from the bottom of the pan. Return the seared chicken and any accumulated juices back into the skillet. Bring the liquid to a gentle boil, then reduce the heat to low. Cover the pan and simmer for 10-12 minutes, or until the orzo is tender and most of the liquid has been absorbed.
Remove the lid and stir in the fresh baby spinach, Parmesan cheese, lemon juice, and lemon zest. Stir constantly for about a minute until the spinach has wilted and the cheese has melted into a creamy sauce. Taste and add more salt or pepper if needed. Garnish with fresh parsley before serving.