Preheat oven to 375°. In a large heatproof skillet over medium-high heat, heat oil. Generously season chicken with salt and black pepper and cook, turning occasionally, until golden brown, 4 to 5 minutes per side. Transfer chicken to a plate and pour off half of fat from skillet.

Return skillet to medium heat. Cook garlic and thyme, stirring occasionally, until fragrant, about 1 minute. Stir in broth, tomatoes, cream, and Parmesan; season with salt. Bring to a simmer, then return chicken to skillet.

Transfer skillet to oven and bake until chicken is cooked through and an instant-read thermometer inserted into the thickest part registers 165°, 10 to 12 minutes.

Divide chicken among plates. Top with basil.