Debone the chicken into 8 pieces, keeping the wing tips. Cut the carcass into a few medium-sized pieces.

In a large saucepan, heat a splash of olive oil over medium heat. Brown the chicken carcass and wing tips all over, then add the onion skins.

Trim the stems of the button mushrooms and add them to the chicken carcass and onion skins. Slice the mushroom caps into 6 pieces for small ones and 8 for larger ones.

Sauté the mushrooms for about 2 minutes until they begin to turn a light golden color.

Pour in the chicken stock along with the dried porcini mushrooms, bay leaf, thyme, and garlic cloves. Let it gently simmer for 10-15 minutes to infuse the flavors into the stock. Strain and set aside.

Pat the chicken pieces dry with kitchen paper. Heat a wide sauté pan over medium-high heat and add 2 tablespoons of olive oil. Season the chicken skin with fine salt and place them skin side down in the pan.

Press the chicken down with a heavy pan and fry for about 5 minutes until the skin is deeply golden. Flip the chicken pieces over for 1 minute to lightly brown the flesh side, then remove and set aside.

Lower the heat to medium and add the butter and shallots to the pan. Sweat gently, using a wooden spoon to scrape up the browned bits from the bottom of the pan as they cook.

Increase the heat and add the mushrooms, frying until they start to release their moisture and turn a light golden color.

Raise the heat to medium-high and pour in the white wine, scraping up any remaining bits, and simmer until reduced by two-thirds.

Once the white wine has reduced, arrange the chicken pieces in the pan skin side up. Ladle the stock into the pan until it reaches just below the chicken skin.

Reduce the heat to medium-low, cover with a cartouche, and simmer gently for about 20 minutes or until the chicken is cooked through and reaches 70°C.

Meanwhile, in a separate pan, gently reduce the double cream over medium heat by about a third until it thickens slightly.

Once the chicken is cooked, transfer it to a heatproof tray to keep warm. Stir the reduced cream into the sauce, whisking to emulsify, and continue to reduce until you have a light sauce.

In a small bowl, whisk the egg yolks with the dijon mustard and lemon juice. Temper this mixture by whisking in a few spoons of the hot sauce before stirring it back into the pan off the heat.

Melt the butter in a pan over medium heat until the solids turn golden and the butter has a biscuity aroma. Brush this brown butter over the chicken skin and place the tray under the grill until the skin is extra crispy.

Return the chicken to the sauce to warm through gently over low heat. Taste and adjust the seasoning, adding more lemon juice if needed for acidity.

Finish with chopped parsley and serve.