Dice the onion and celery, mince the garlic, slice the carrots, and cut the baby potatoes in half. Cut the chicken thighs into 1-inch pieces and sprinkle them with 2 tablespoons of flour.
Heat butter and olive oil in a large pot over medium heat. Brown the flour-coated chicken on all sides, then remove it to a bowl.
In the same pot, sauté the onion, celery, garlic, and carrots until softened, about 5-7 minutes.
Add the remaining flour to the vegetables and sauté for 2 minutes.
Return the chicken to the pot and add potatoes, dried herbs, pepper, chicken broth, and vegetable broth. Stir to combine and bring to a boil.
Lower the heat to medium-low and simmer uncovered for about 30 minutes until the potatoes are tender and the broth thickens. Adjust salt as needed and serve hot, garnished with fresh parsley if desired.