Heat the olive oil in a large nonstick or cast-iron skillet over medium-high heat until shimmering.
Add the cubed chicken, 1/2 teaspoon salt, and black pepper. Cook for about 5 minutes, stirring occasionally, until the chicken is lightly browned and cooked through. Transfer it to a clean plate.
Reduce the heat to medium. Add the chopped turkey ham and cook for 3–4 minutes, stirring occasionally, until lightly browned. Transfer it to the plate with the chicken.
Add the Brussels sprouts, sweet potato, onion, and remaining 1/2 teaspoon salt to the skillet. If the pan seems dry, add a small drizzle of olive oil. Cook for about 10 minutes, stirring occasionally, until the vegetables begin to soften and brown.
Stir in the apples, garlic, thyme, and cinnamon. Cook for about 30 seconds, just until fragrant.
Pour in 1/2 cup chicken broth. Bring to a gentle boil and cook for about 2 minutes, allowing some of the liquid to reduce.
Return the chicken to the skillet and pour in the remaining 1/2 cup broth. Cook for another 2–4 minutes, or until the chicken is hot and the sweet potatoes are tender.
Stir the turkey ham into the Harvest Chicken Skillet and cook briefly until everything is warmed through. Serve hot.