Preheat your oven to 375°F (190°C).

Pat the chicken pieces dry with paper towels and season them generously with salt and pepper.

Heat the olive oil in a large, oven-safe skillet or Dutch oven over medium-high heat. Sear the chicken, skin-side down, until the skin is crispy and golden brown, about 5-7 minutes.

Flip the chicken and sear the other side for an additional 3-4 minutes. Transfer the partially cooked chicken to a plate and set aside.

Reduce the heat to medium and add the sliced mushrooms to the same skillet. Sauté the mushrooms, stirring occasionally, until they release their moisture and begin to brown, about 5-7 minutes.

Add the minced shallots to the skillet and cook for an additional 2-3 minutes, until fragrant.

Deglaze the pan by pouring in the cognac or brandy, scraping up any browned bits from the bottom of the skillet. Allow the alcohol to simmer and reduce by half, about 2-3 minutes.

Pour in the heavy cream and stir to combine. Bring the sauce to a gentle simmer and let it thicken slightly, about 5 minutes.

Season the sauce with salt, pepper, and the ground nutmeg.

Return the seared chicken to the skillet, nestling it into the sauce.

Transfer the skillet to the preheated oven and roast the chicken until it's cooked through, with an internal temperature of 165°F (74°C), about 30-40 minutes.

Remove the skillet from the oven and let the chicken rest for 5-10 minutes.

Garnish the Hunter Chicken with fresh thyme leaves and chopped parsley before serving.