Reduce heat to medium-low. Add tomatoes, garlic, salt and pepper; cook, scraping the bottom of the pan to loosen any browned bits, until the tomatoes begin to burst, 4 to 5 minutes. Add broth; increase heat to high and cook, stirring often, until slightly reduced, about 3 minutes, pressing on the tomatoes as needed to crush them. Add the pasta and chicken; toss gently to combine. Divide the pasta mixture among 4 bowls. Drizzle evenly with balsamic glaze; sprinkle with Parmesan and basil.