In a large stock pot or dutch oven, add the broth, onion, carrots, celery, garlic, and salt. Bring this to a boil then reduce the heat and let it simmer until the veggies are tender. Transfer all the softened veggies to a blender along with about a cup of broth. Blend until smooth. See notes for safely blending hot liquid.
Add the liquid back into the pot (option to run the blended veggies through a sieve first) and stir. Add the thyme, bay leaves, and the cheese rind. Cover, and allow the broth to come to a boil, over medium heat.
Once boiling, add the pastina to the broth. Bring the heat down to low, and let the pasta cook until tender, about 18-20 minutes, or whatever the pastina packaging calls for. Stir occasionally.
Add the shredded chicken to the pasta 3 minutes before you finish cooking. Remove the thyme sprig, bay leaves and parmesan rind. Remove from heat and serve immediately. Enjoy!