1. In a shallow dish, combine 1/4 cup of the flour with 1/2 teaspoon each of salt and black pepper. Dredge the chicken thighs in the flour mixture to coat completely, then set on a plate.
2. In a 12-inch nonstick skillet over medium-high, heat the olive oil. Add the chicken thighs and cook until well browned, 3 to 4 minutes on each side. Transfer to a clean plate and set aside.
3. Add the bacon to the skillet and cook, stirring often, for 2 minutes. Add the onion, carrots and mushrooms and saute until the vegetables begin to brown, about 4 minutes. Sprinkle the remaining 3 tablespoons flour over the vegetables and cook, stirring constantly, for 2 minutes more.
4. Add the stout and broth to the pan and bring to a boil using a wooden spoon to scrape up any browned bits from the bottom of the pan. Return the thighs to the pan, nestling them among the vegetables. Reduce the heat until the liquid is gently simmering, then cover and cook for 15 minutes.
5. Add the peas and cook, covered, for 5 minutes. Uncover the pan and simmer for 5 minutes more. Season with salt and pepper and serve the chicken with vegetables and sauce spooned over the top.
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