Heat the same sauté pan you used to cook the chicken over medium-to-high heat. Add 1 tbsp. of olive oil and the chopped garlic and shallots to the pan and sauté for 1-2 minutes or until translucent. Add the mushrooms, rosemary, and a pinch of salt and pepper and cook, stirring constantly, until ingredients begin to brown, about 4 minutes. Add balsamic vinegar and cook until reduced by about half. Add the cooked chicken and tomatoes (with juice), then simmer, breaking up tomatoes with a spoon and stirring occasionally, until sauce is just thickened, about 15 minutes. Add the cooked pappardelle and mix together to incorporate ingredients and to warm the pasta. Add salt and pepper, to taste, if needed.