In a large Dutch oven or similar thick, sturdy pot, heat the olive oil over medium-high heat. Once hot, add the chicken, along with salt and pepper. Sauté until the chicken is lightly browned on all sides and fully cooked, which should take about 4 minutes. Remove the chicken to a plate and set aside.
Reduce the heat to medium and add the butter to the pot. Once melted, toss in the carrots, celery, and onion. Sauté these vegetables until they start to soften, about 7 minutes. You’ll know they’re ready when the onion is translucent.
Sprinkle the flour over the sautéed vegetables. Stir constantly for about 2 minutes. Look for the flour to turn a golden color and ensure no white bits remain, which indicates it’s cooked properly.
Add in the garlic and continue to cook while stirring for another 30 seconds. The aroma will be delightful and invigorating.
Gradually pour in 3 cups of the chicken stock and the milk, stirring constantly to prevent lumps. This step is crucial for achieving a smooth texture.
Now, toss in the potato, sweet potato, red bell pepper, 1 teaspoon of thyme, the bay leaf, and the remaining teaspoon of salt. Bring the mixture to a gentle simmer.
Let the stew simmer gently for about 15 minutes. Keep an eye on it, adjusting the heat to ensure it simmers without boiling rapidly. Give it an occasional stir to prevent sticking.
After 15 minutes, stir in the browned chicken. Continue to simmer until the vegetables are tender and the stew thickens slightly, around another 15 minutes. If it gets too thick, feel free to add more chicken stock to reach your desired consistency.
Just before serving, stir in the lemon juice, Parmesan, and the remaining teaspoon of thyme. Remember to remove and discard the bay leaf. Taste, then adjust seasoning as needed.
Serve hot, garnished with a sprinkle of Parmesan and a dash of black pepper. Enjoy the warm embrace of this Chicken Stew!