Pre-heat the pressure cooker on the BROWN setting
Add the bacon and cook until crisp. Remove the bacon with a slotted spoon and set it aside. Pat the chicken dry and generously season with salt and pepper. Sear in batches until browned on all sides. Remove the browned chicken to a plate and set aside.
Add the sliced onions and sauté until the onions are lightly browned. Add the garlic and carrots and cook for another 2 minutes. Add the thyme, bay leaf and rosemary. Pour in ½ cup of the brandy and deglaze the pan by scraping up any brown bits on the bottom of the cooker. Pour in the red wine, chicken stock, and diced tomatoes and bring the mixture to a simmer. Return the chicken and any juices on the plate to the cooker and lock the lid in place.
Pressure cook on HIGH for 10 minutes.
Release the pressure from the pressure cooker manually and carefully remove the lid. Transfer the chicken to a deep serving vessel.
Mix the remaining 3 tablespoons of the butter with the flour, making a paste (called a beurre manié). Return the pressure cooker to the BROWN setting and bring the braising liquid to a boil. Stir the beurre manié into the braising liquid to thicken. Add the sautéed pearl onions and mushrooms and season to taste with salt and pepper. Pour the sauce and vegetables over the chicken in the serving vessel, sprinkle with the fresh thyme and cooked bacon and serve.
Tip – To making peeling fresh pearl onions easier, trim the root and stem. Blanch them in boiling water for a couple of minutes before peeling.