Cook the pasta according to the package directions. Drain, reserving 1/2 cup pasta water. While the pasta is cooking, heat the oil over a medium heat in a large, heavy skillet. Add the garlic and tomatoes and cook until the garlic is soft but not browned, about 2 minutes. Add the chicken and cook, stirring a few times, until just cooked through, about 5 minutes. Add the arugula, radicchio, endive, broth, salt, and pepper, and cook until the greens are wilted, 1 to 2 minutes. Add pasta water, as necessary, for a wetter sauce.
Combine the pasta and vegetable mixture in the pasta pot and toss to combine. Add the basil just before serving. Garnish with shaved Parmesan and a sprinkling of basil.
Excellent Source of: Calcium, Fiber, Folate, Iron, Manganese, Niacin, Phosphorus, Potassium, Vitamin A, Vitamin C, Vitamin K, Protein