Season the chicken all over generously with salt and pepper. Place the chicken in a large bowl. Cover it with the wine and chicken stock. Add the fresh thyme into the bowl. Cover and refrigerate. Marinate for at least 2 hours, or overnight.
When you’re ready to make the dish, heat the pancetta in a large pot or dutch oven over medium heat. Cook until crispy and the fat is rendered, about 10 minutes. Remove the pancetta with a slotted spoon and place it on a paper towel to drain excess grease.
Remove the chicken from the wine (keep the wine marinade!) and pat the chicken completely dry. Add the chicken to the same pot with the fat from the pancetta and sear on all sides. You may need to do this in batches! Sear for about 3 to 4 minutes total, just until all sides are deeply golden. Remove the chicken and place it on a plate.
With the heat over medium-low, add the 2 tablespoons of butter. Stir in the onions, carrots and garlic with a pinch of salt and pepper. Cook until softened, about 5 minutes. Stir in the mushrooms. Cook until those soften, another 5 to 6 minutes. Stir in the tomato paste and cook for 2 minutes. Stir in the flour and cook for 2 minutes more.
Deglaze the pan with the brandy, adding it and stirring, cooking for 1 to 2 minutes. Stir in the remaining wine marinade from the chicken. Bring the mixture to a boil. Cook, stirring often, until the mixture reduces by half, about 10 to 12 minutes.
Add the chicken and the pancetta back to the pot. Reduce the heat to low, just so it’s barely simmering. Cover the pot and cook for 45 to 60 minutes, turning the chicken halfway through. Taste and season with more salt and pepper if necessary.
When the dish is almost finished, heat the 1 tablespoon of butter in a skillet. Once melted, stir in the pearl onions with the sugar and salt. Cook, stirring often, until the onions are caramelly, about 10 minutes. Remove the onions from the skillet and add them to the pot with the chicken.
In the same skillet where you cooked the onions, add the sourdough slices and toast them. If needed, you can add in another tablespoon or so of butter - or just butter the bread and toast it until golden.
Sprinkle the chicken dish with the chopped parsley. Serve the chicken with the sauce and vegetables, along with the bread for dipping.