Preheat oven to 375°. In a large oven-safe skillet over medium-high heat, heat 1 tablespoon oil. Season chicken generously with salt and pepper then dredge in flour. Sear until golden, 5 minutes per side. Transfer chicken to a plate.

Return skillet to medium heat and add remaining 2 tablespoons oil. Stir in onions and saute till just browned. Add garlic, thyme, and red pepper flakes, and cook until fragrant, 1 minute. Stir in broth, heavy cream, sun-dried tomatoes. Bring to a simmer, then return chicken to skillet.

Either finish stove-top or transfer skillet to oven and bake until chicken is cooked through (and juices run clear when chicken is pierced with a knife), 10 to 12 minutes.

Garnish with basil and serve.