Heat olive oil and butter in a large cast-iron skillet over medium-high heat. Season chicken pieces generously with salt and pepper, then sear them skin-side down for 4-5 minutes until golden brown. Flip and sear another 3-4 minutes, then remove to a plate.

In the same skillet, add diced onion and cook for 2-3 minutes until softened, stirring occasionally. Add minced garlic and cook for another 30 seconds until fragrant and the vegetables release their aromas.

Add cubed butternut squash to the skillet and stir gently, coating everything with the oil. Sprinkle in sage, thyme, paprika, and nutmeg, allowing the spices to bloom for 1 minute until your kitchen smells like autumn.

Pour in apple cider and chicken broth, stirring to deglaze the pan and combine flavors. Return the chicken pieces to the skillet, nestle them among the butternut squash, and bring everything to a gentle simmer.

Reduce heat to medium and simmer uncovered for 12-15 minutes until the butternut chicken is nearly cooked through and the squash begins to soften. Stir in heavy cream and fresh spinach, cooking for 2-3 minutes more until it becomes tender and the cozy fall skillet chicken butternut reaches a rich, creamy consistency.

Taste and adjust seasoning with additional salt, pepper, or spices as needed. The sauce should coat the back of a spoon and the chicken should reach an internal temperature of 165°F.