How to Make It
Preheat the oven to 400°. Set the tomatoes, cut side up on a large baking sheet. Drizzle with the olive oil and season with salt and pepper. Bake the tomatoes for about 45 minutes, or until very soft and lightly browned. Peel the tomatoes and transfer them to a medium bowl.
In a medium saucepan, cover the chicken breasts with 3 cups of water and bring to a simmer over low heat until just cooked through, about 15 minutes. Cut the chicken crosswise into thin slices and cover with plastic wrap to keep the meat moist. reserve 1/4 cup of the cooking broth.
Meanwhile, bring a large pot of salted water to a boil. Add the escarole and cook over high heat until just tender, about 4 minutes. Using a slotted spoon, transfer the escarole to a colander. Bring the water back to a boil and add the fusilli. Cook until al dente, about 8 minutes. Drain the fusilli, leaving a little cooking water to keep the pasta moist, and return it to the saucepan; keep warm.
Pour the reserved chicken broth into a large skillet. Add the garlic and cook over moderately high heat for 30 seconds. Add the escarole and stir to blend with the garlic. Season with salt and pepper. Add the roasted tomatoes with their accumulated juices and the sliced chicken and cook until heated though. Stir in the rosemary. Add the roasted tomato mixture to the fusilli and toss well, then season with salt and pepper. Transfer the pasta to a large platter and sprinkle with the basil and Parmesan cheese. Serve at once.