Preheat the oven to 375°F (190°C).
In a large ovenproof skillet over medium-high heat, heat 1 tablespoon of olive oil. Generously season the chicken breasts with salt and black pepper, then cook them, turning halfway through, until golden brown (about 5 minutes per side). Transfer the chicken to a plate.
In the same skillet over medium heat, add the remaining 2 tablespoons of olive oil. Stir in the garlic, thyme, and crushed red pepper flakes. Cook, stirring, until fragrant (about 1 minute).
Stir in the chicken broth, sun-dried tomatoes, cream, and grated Parmesan. Season with salt. Bring the mixture to a simmer, then return the chicken and any accumulated juices to the skillet.
Transfer the skillet to the oven and bake the chicken until it’s cooked through and the juices run clear when pierced with a knife (10 to 12 minutes).
Arrange the chicken on a platter, spoon the sauce over it, and top with torn fresh basil.
Plate the Marry Me Chicken with extra sauce.
Pair it with your favorite sides (rice, roasted veggies, bread, salad, pasta, or mashed potatoes).
Serve hot and enjoy.