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Arrange a rack in center of oven; preheat to 375°. In a large ovenproof skillet over medium-high heat, heat 1 Tbsp. oil. Generously season chicken with salt and black pepper and cook, turning halfway through, until golden brown, about 5 minutes per side. Transfer chicken to a plate.
In same skillet over medium heat, heat remaining 2 Tbsp. oil. Stir in garlic, thyme, and red pepper flakes. Cook, stirring, until fragrant, about 1 minute. Stir in broth, tomatoes, cream, and Parmesan; season with salt. Bring to a simmer, then return chicken and any accumulated juices to skillet.
Transfer skillet to oven. Bake chicken until cooked through and an instant-read thermometer inserted into thickest part registers 165°, 10 to 12 minutes.
Arrange chicken on a platter. Spoon sauce over. Top with basil.