Prepare the vegetables by dicing the onion and celery, mincing the garlic, slicing the carrots, and halving the baby potatoes.
Cut the chicken thighs into 1-inch pieces.
Sprinkle 2 tablespoons of flour over the chicken and toss until evenly coated.
Heat butter and olive oil in a large pot over medium heat until hot and sizzling.
Add the chicken to the pot and let it brown on all sides without stirring too much.
Once browned, remove the chicken with a slotted spoon and set aside.
Add the onion, celery, garlic, and carrots to the same pot and sauté until the onions soften.
Scrape up the browned bits from the bottom as the vegetables release moisture.
Once the vegetables have softened slightly, sprinkle in the remaining 2 tablespoons of flour and cook for about two minutes, allowing it to coat the bottom of the pot again.
Return the browned chicken to the pot, then add the potatoes, parsley, thyme, rosemary, sage, pepper, chicken broth, and vegetable broth.
Stir well to dissolve any flour stuck to the bottom.
Cover the pot and bring the stew to a boil.
Once boiling, remove the lid, reduce the heat to medium-low, and let the stew simmer uncovered for about 30 minutes, stirring occasionally.
Check the potatoes for tenderness and ensure the broth has thickened to your desired consistency.
Taste the stew and add salt if necessary, depending on the salt content of your broth.
Garnish with freshly chopped parsley if desired, then serve hot and enjoy.