Preheat your oven to 375°F (190°C). Adjust your oven racks so your skillet can fit in the center.
Prepare your chicken breasts on a cutting board. Trim any excess parts, then use paper towels to pat them dry on all sides.
Season your chicken breasts generously with salt and black pepper on both sides. Set them aside for a moment.
Heat a cast-iron skillet over medium-high heat. Once it’s warm, add olive oil and ensure it covers the entire surface of the skillet.
When the oil is hot and shimmering, add your seasoned chicken breasts. Sear each side for 3 to 4 minutes until they’re golden. Remove the partially cooked chicken breasts and set them aside on a plate.
Lower your skillet’s heat to medium-low and add minced garlic, sautéing it until it becomes fragrant, about 1 to 2 minutes.
Pour in the chicken broth, stirring to lift any browned bits from the bottom of the skillet.
Transfer the skillet to a cooler burner and let it cool slightly before you add the heavy cream. Gently stir until it blends with the chicken broth.
Sprinkle in your freshly grated Parmesan cheese, stirring until it has melted into the sauce.
Bring your skillet back to the hot burner, add in the sun-dried tomatoes, dried oregano, and red pepper flakes, stirring gently to combine.
Once your sauce is simmering, return your seared chicken breasts to the skillet, flipping them to coat all sides in the creamy sauce.
