Meanwhile, pulse the tomatoes in a food processor until coarsely ground and no large pieces remain, about 12 pulses. Cook oil, garlic, oregano, pepper flakes, and 1/4 teaspoon salt in 12-inch ovensafe skillet over medium-high heat until fragrant, about 1 minute. Stir in processed tomatoes, water, 1 cup broth, and pasta. Cover and cook at vigorous simmer, stirring often, until pasta is tender, about 15 minutes.

Stir in remaining 1/2 cup broth. Season with salt and pepper to taste. Scatter sliced chicken evenly over top and sprinkle with cheese. Transfer skillet to oven and bake until cheese has melted and chicken is crisp, 5-10 minutes. Sprinkle with basil and serve.