Pat the chicken breasts dry with paper towels to ensure crispy skin. Season generously with salt and pepper on both sides.
Heat a large ovenproof skillet over medium-high heat and add olive oil. When the oil shimmers and just starts to smoke, carefully place the chicken breasts skin-side down into the hot pan.
Sear the chicken without moving for about 3 minutes, until the skin is golden brown and crispy. Flip the chicken using tongs and sear the other side for another 1-2 minutes.
Transfer the skillet to a preheated oven at 200°C (400°F) and roast the chicken for 15-20 minutes, until the internal temperature reaches 65°C (150°F). The meat should be juicy and opaque.
While the chicken roasts, prepare the sauce: in a small bowl, whisk together Dijon mustard and lemon juice. Set aside.
Once cooked, remove the skillet from the oven and transfer the chicken to a plate. Cover loosely with foil and let rest for 5 minutes.
While the chicken rests, pour off excess fat from the skillet, leaving about a tablespoon. Add minced garlic and thyme to the pan, sauté over medium heat until fragrant, about 30 seconds.
Deglaze the pan with the cream, scraping up any browned bits from the bottom. Stir in the Dijon-lemon mixture and simmer gently until the sauce thickens slightly, about 3 minutes.
Slice the rested chicken breasts and arrange them on a serving platter. Spoon the creamy sauce over the top and sprinkle with chopped parsley for a fresh burst of color.
Serve immediately, enjoying the crispy skin, juicy meat, and bright, velvety sauce that ties everything together.
