Start by patting the chicken breasts dry and seasoning them generously with salt and pepper. Heat oil in a large skillet over medium-high heat until shimmering, then add the chicken. Sear for about 4-5 minutes on each side until golden brown and cooked through, then transfer to a plate and cover loosely with foil to keep warm.
In the same skillet, add sliced mushrooms and cook until they turn golden and fragrant, about 5 minutes. Then, add the minced garlic and cook for another 30 seconds until aromatic.
Pour in the white wine, scraping up the browned bits from the bottom of the pan, and simmer until the wine reduces by half, about 3 minutes. This builds depth in the sauce.
Stir in the heavy cream and add a pinch of freshly grated nutmeg. Bring the mixture to a gentle simmer, stirring constantly, until the sauce thickens slightly and becomes velvety, about 4 minutes.
Return the chicken breasts to the skillet, nestling them into the sauce. Spoon some sauce over the top and cook on low heat for another 5 minutes until heated through. Check that the internal temperature reaches 75°C (165°F) with a thermometer.
Remove the skillet from heat and let the chicken rest for about 3 minutes. This helps to lock in the juices, keeping the chicken tender and moist.
Garnish with chopped fresh parsley and spoon the luscious sauce and mushrooms over the chicken. Serve immediately with your favorite sides, such as buttery potatoes or crusty bread.
