Equally delicious warm or at room temperature, this pasta dish is great for a picnic.
Preheat oven to 425 degrees. In an 8-inch square baking dish, toss cherry tomatoes with 3 tablespoons oil; season with salt and pepper. Roast until bursting and charred in spots, 20 to 30 minutes. Meanwhile, on a rimmed baking sheet, toss bread with 2 tablespoons oil and Pecorino Romano; season with salt and pepper. Roast, tossing halfway through, until golden brown and crisp, about 12 minutes.
Toss diced tomatoes, basil, and mint with remaining 2 tablespoons oil; season with salt and pepper. Bring a large pot of salted water to a boil. Add pasta; cook according to package directions until al dente. Reserve 1 cup liquid; drain.
Return pasta to pot; toss with roasted tomatoes, their oil, and 1/2 cup reserved pasta water. (Tomatoes should coat pasta but not create much of a sauce.) Season with salt and pepper. Divide among plates, then give each a dollop of ricotta, a spoonful of fresh-tomato mixture, and a sprinkle of croutons. Serve, garnished with a sprig or two of herbs, a generous drizzle of oil, and some cheese and pepper.