Season the chicken pieces with salt and pepper. Heat the olive oil in a large skillet over medium-high heat. Add the chicken and sear until golden brown, about 3-4 minutes per side. Transfer the chicken to a plate and set aside.
In the same skillet, melt the butter over medium heat. Add the chopped onion and cook until translucent, about 2-3 minutes. Stir in the minced garlic and cook for another minute until fragrant.
Add the cubed butternut squash to the skillet and sauté for about 5 minutes, until it starts to soften.
Pour in the chicken broth and bring the mixture to a boil. Stir in the orzo, reduce the heat to low, cover, and simmer for 10 minutes.
Return the chicken to the skillet along with any accumulated juices. Add the fresh thyme and a pinch of nutmeg, then cover and cook for an additional 5 minutes, or until the orzo is tender and the chicken is cooked through.
Stir in the heavy cream and Parmesan cheese until well combined and heated through. Gently fold in the spinach and cook just until wilted, about 1-2 minutes.
Taste and adjust seasoning with additional salt and pepper if needed. Serve hot, garnished with extra Parmesan cheese and thyme leaves if desired.