Sear the Chicken
Warm 1 tablespoon of oil in a large Dutch oven over medium-high heat. Pat the chicken dry and season generously with salt and pepper. When the oil shimmers, place the chicken skin-side down and cook, undisturbed, for 5 to 7 minutes until the skin achieves a rich golden hue. Transfer the seared chicken to a plate and set aside.
Cook the Vegetables
Lower the heat to medium and add the diced onion and carrots to the pot. Sauté for 4 to 5 minutes, stirring frequently, until the vegetables soften and release their aroma. Scrape any browned bits from the bottom of the pot to capture their flavor. Add the remaining tablespoon of oil, followed by the flour, stirring until the mixture is fragrant and well combined, about 2 minutes.
Add the Remaining Ingredients
Dissolve the chicken base in 1 cup of hot water and pour it into the pot, deglazing as you stir. Return the chicken along with any accumulated juices. Add the remaining 5 cups of water and the thyme, if using. Bring to a gentle boil over medium-high heat, then stir in the sweet potatoes.
Simmer and Finish
Reduce the heat to low, cover, and allow the stew to simmer for about 25 minutes, or until the chicken reaches an internal temperature of 165°F. Remove the pot from the heat and transfer the chicken to a cutting board. Let it rest for 10 minutes, discard the skin, and shred the meat. Remove the thyme stems if present, return the shredded chicken to the pot, and adjust seasoning with salt and pepper. Serve hot and enjoy.