Dice the onion and celery, mince the garlic, slice the carrots, and cut the baby potatoes in half before you begin.
Cut the chicken thighs into 1-inch pieces. Sprinkle 2 tablespoon flour over the chicken and toss until the chicken is evenly coated.
Add the butter and olive oil to a large pot. Heat the butter and oil over medium until they are hot and sizzling.
Add the flour-coated chicken to the pot with the butter and oil and allow the chicken to brown on all sides. Remove the chicken to a clean bowl with a slotted spoon.
Add the onion, celery, garlic, and carrots to the pot and sauté until the onions are soft.
Once the vegetables are slightly softened, add the remaining 2 tablespoon flour to the pot and continue to sauté over medium for about two minutes more.
Return the browned chicken to the pot. Add the potatoes, parsley, thyme, rosemary, sage, pepper, chicken broth, and vegetable broth. Stir to combine.
Place a lid on the pot and allow it to come up to a boil. Remove the lid and turn the heat down to medium-low. Allow the stew to simmer for about 30 minutes.
Taste the stew and add salt if needed. Add a tablespoon of fresh chopped parsley if desired, and serve hot.