Preheat the oven to 350F.
Remove any excess moisture from the chicken by blotting it with a paper towel. Sprinkle both sides of the chicken generously with salt and pepper.
Heat the olive oil over medium heat in a large pan or skillet (cast iron is best). Add the chicken thighs skin side down, and cook for 4-6 minutes until the skin turns golden brown. Move the chicken slightly in the pan every 2 minutes to encourage even browning.
Turn the thighs over and brown the other side for 3-4 minutes. Transfer the chicken to a plate.
Add the potatoes, carrots, and thyme to the pan, sprinkle with salt and pepper, and cook the vegetables until they turn golden, 5-10 minutes, stirring occasionally so they cook evenly and don't burn.
Add the onions and garlic once the potatoes and carrots start to brown, cooking until they also soften a bit and turn color.
Pour in the wine, toss with the vegetables and simmer for 2 minutes. Add the flour and stir it into the vegetables for about 2 minutes to cook off the raw taste and allow it to develop some flavor. Don't let it burn.
Pour in the chicken stock, bring to a high simmer, and add the chicken back to the pan. Remove from the heat and place the pan in the oven on the bottom rack, covered, and cook for 35-40 minutes. If you don't have a proper lid for your pan, use aluminum foil.
Remove the pan from the oven, and garnish the chicken with fresh parsley. Enjoy!