Pat chicken pieces dry with a paper towel and season well with salt and pepper.
Heat the olive oil over medium heat in a large pot. Add the bacon and cook until crispy. Transfer bacon with a slotted spoon to a plate lined with paper towels.
Add the chicken pieces in batches of two to the leftover bacon grease (skin side down). Sear for undisturbed for 4 minutes, check to see if the skin is crispy and browned, if so flip and repeat on the other side (if not allow another minute or two and flip when browned). Transfer chicken to the plate with the bacon. Set aside.
Add the onions and carrots to the pan and cook over medium heat for 5 minutes, while stirring occasionally, until the onions are transparent and lightly browned.
Add the garlic and cook another minute.
Add the tomato paste. Cook the tomato paste until it is fragrant and begins to darken. Pour in the brandy and wine scraping the bottom to remove any stuck-on bits. Allow to reduce by half.
Pour in chicken stock; stir to combine. Add the bacon, chicken, and any juices leftover from the plate back into the pot with the bay leaves. Season with salt and pepper, cover the pot, turn the heat to low, and simmer for 20 minutes or until the chicken is cooked through and no longer pink in the middle.
While chicken cooks melt 2 tablespoons of butter in a pan over medium heat. Cook the mushrooms for 8 to 10 minutes, until soft and browned. Set aside.
If the sauce looks fatty, don't stir it into the sauce. Remove the fat by running a spoon over the surface just enough to allow the fat, but not the sauce, to spill into the spoon. Repeat until there's no more visible fat.
Mash the butter with the flour and stir into the pot (the heat will cook any lumps out). Add the pearl onions and the mushrooms; bring to a simmer and cook for a further 10 minutes, until the sauce has thickened. Taste for seasoning and add more salt as needed.
Discard the skin and bay leaves before serving.
When searing the chicken, start with a hot pan and don't overcrowd the chicken in the pan. This will cause steaming instead of browning.
Taste your bacon once it's cooked, if it's salty go light on the salt then taste before serving and adjust the seasoning accordingly.
For Crispy Skin: Cook in the oven instead of on the stove. use a more shallow pan that allows the skin to sit slightly above the sauce. Bake covered at 350°F for 20 minutes then raise the heat to 400°F and cook uncovered for a further 10 minutes. Thicken on the stove with the chicken removed from the pan.