Heat the butter (1 tbsp) and olive oil (1 tbsp) in a roasting tin over a medium to high heat.
Fry the chicken thighs, skin-side down, for 5 minutes until golden brown, then turn them over and fry for a further 3 minutes.
Remove the chicken and set it aside.
Sauté the onion and carrot in the frying fat for 5 minutes.
Add the garlic and tomato purée (1 tbsp) and fry for 1 minute.
Deglaze with cognac (2 tbsp) and reduce briefly.
Pour in the red wine (300 ml) and reduce by half.
Add the chicken stock (200 ml), thyme (3 sprigs) and bay leaf (1).
Place the chicken in the roasting tin, skin-side up, so that it is half-submerged in the sauce.
Cover the roasting tin with the lid and leave to braise in the oven for 1 hour.
Whilst the chicken is braising, fry the bacon in a frying pan for 4 minutes until crispy, then remove it.
Fry the button mushrooms in the bacon fat for 5 minutes until well browned, season with salt and pepper, then remove them from the pan.
Melt the butter (1 tbsp) in a frying pan, add the pearl onions with the sugar (1 tsp) and glaze for 8 minutes over a medium heat until they are golden brown.
Remove the roasting tin from the oven and take out the sprigs of thyme and the bay leaf.
Remove the chicken and keep it warm.
Simmer the sauce uncovered for 8 minutes until it is slightly thickened, then season to taste with salt and pepper.
Add the bacon, mushrooms and pearl onions to the sauce.
Return the chicken to the sauce and leave to simmer for 5 minutes over a low heat.