Preheat your oven to 375°F (190°C). Pat the chicken completely dry with paper towels and season all over with the salt and black pepper.
Heat the olive oil in a large oven-proof skillet over medium-high heat. Place the chicken skin-side down and sear for 5-7 minutes until golden brown and crispy. Flip and cook for 3 more minutes. Remove from the skillet and set aside on a plate.
Reduce the heat to medium. Add the butter to the skillet and let it melt. Add the minced garlic and sauté for 1 minute until fragrant.
Pour in the chicken broth, using a wooden spoon to scrape up any browned bits from the bottom of the pan. Stir in the heavy cream, Parmesan cheese, and fresh dill. Allow the sauce to simmer for 3 minutes, stirring occasionally, until it slightly thickens.
Return the chicken to the skillet, placing them skin-side up so the skin remains crispy. Transfer the skillet directly into the preheated oven.
Bake for 25-30 minutes, or until the chicken is cooked through and registers 165°F (74°C) on an instant-read meat thermometer. Serve hot, spooning the extra sauce over the top of the meat.