Pat the chicken thighs dry with paper towels, then season generously with salt, pepper, and some chopped thyme.
Heat the skillet over medium-high heat and add a tablespoon of olive oil. When shimmering, place the chicken thighs skin-side down.
Cook the chicken skin until crispy and golden brown, about 5-7 minutes. Flip and cook the other side for another 5 minutes, then remove the chicken and set aside.
Reduce the heat slightly and add minced garlic to the pan, stirring until fragrant, around 30 seconds. Scrape up any browned bits from the bottom.
Add the sweet potatoes and sliced apples to the pan, tossing to coat in the garlic and rendered chicken fat. Cook for about 5 minutes, turning occasionally, until slightly softened and fragrant.
Sprinkle cinnamon and remaining thyme over the produce, mixing evenly. Pour in the chicken broth, then nestle the chicken thighs back into the skillet, skin-side up.
Bring the mixture to a gentle simmer, then cover the skillet and cook for 20-25 minutes, until the sweet potatoes are tender and the chicken is cooked through.
Uncover the skillet and increase the heat to medium. Let the sauce simmer uncovered for 3-5 minutes, stirring occasionally, until slightly thickened and glossy.
If desired, stir in a tablespoon of butter for added richness and shine, allowing it to melt into the sauce.
Adjust seasoning with salt and pepper to taste, then remove from heat. The chicken should be crispy, the produce caramelized, and the sauce velvety.
Serve the skillet directly at the table for a cozy, rustic presentation—dig in with a side of crusty bread or a simple green salad.