Heat olive oil and 1 tablespoon of butter in a large, deep skillet or Dutch oven over medium-high heat until shimmering. Season chicken pieces all over with salt, pepper, and Italian seasoning. Add in a single layer, working in batches if needed. Sear for 5 to 6 minutes, flipping once or twice, until golden brown on multiple sides. Transfer to a plate and set aside.

Reduce heat to medium and add the remaining 2 tablespoons of butter to the same skillet. Add the sliced mushrooms and diced onion. Cook undisturbed for 2 to 3 minutes to start browning, then stir and continue cooking for 5 to 8 minutes total until mushrooms are browned and onions are soft and translucent. Add minced garlic and cook for 1 minute, stirring constantly, until fragrant.

Add the dry orzo directly to the skillet and stir constantly for about 2 minutes to lightly toast the pasta until slightly golden and aromatic.

Pour in the Marsala wine and use a wooden spoon to scrape up all the browned bits from the bottom of the pan. Let simmer for about 2 minutes, stirring occasionally, until reduced by roughly half.

Add 3.5 cups of chicken broth and stir to combine. Bring to a boil over medium-high heat, then reduce to medium-low to maintain a gentle simmer. Cook uncovered for 10 to 12 minutes, stirring every 2 to 3 minutes, until orzo is tender and most liquid is absorbed. Add remaining broth if orzo is still firm but liquid is gone.

Stir in the heavy cream or Greek yogurt and the freshly grated Parmesan cheese. Mix until the cheese melts and the sauce becomes smooth and velvety. If using Greek yogurt, reduce heat to low before adding.

Add the baby spinach and the seared chicken back into the skillet along with any accumulated juices. Stir for 1 to 2 minutes until the spinach wilts and the chicken is heated through. Taste and adjust seasoning with additional salt and pepper if needed.

Remove from heat and garnish with freshly chopped parsley and extra Parmesan. Serve immediately while hot and creamy.