Preheat your oven to 375°F (190°C). Heat olive oil in a large oven-safe skillet over medium-high heat.
Season the chicken with salt and pepper. Sear skin-side down for 6 minutes until golden brown. Flip and cook for 2 minutes. Remove chicken and set aside.
In the same skillet, add garlic, thyme, and butternut squash. Sauté for 4 to 5 minutes.
Stir in the uncooked orzo and toast for 1 minute. Pour in the chicken broth, scraping the bottom of the pan.
Return the chicken to the skillet, placing it on top of the mixture. Transfer to the oven and roast for 20 minutes until the chicken reaches 165°F and the liquid is mostly absorbed.
Remove from the oven. Temporarily take out the chicken to stir in the heavy cream, parmesan cheese, and fresh spinach. Stir until the spinach wilts, then return the chicken and serve.