Cube the chicken breast and then season with salt and pepper. Heat a large stock pot and drizzle with the olive oil. Add the chicken pieces, don't over crowd so the chicken browns and you get that lovely flavored brown bits on the bottom of the pot and the chicken cooks through. Transfer browned chicken pieces to a plate or a bowl and set aside.
Lower the heat and add the butter to the pot. Once melted add the onions, carrots and celery. Cook for about 5 minutes or so, you want the onion translucent. Add the garlic and the seasoning stirring for about 30 seconds.
Take a few tablespoons of the milk and add the corn starch to make a little slurry. Add this and the rest of the milk to the pot. Add the milk and the Parmesan rind. Simmer for 10 - 15 minutes until the veggies cook through.
Add the gnocchi and the broccoli and bring to a quick boil for 5 minutes. Turn off the heat and add the chicken and the juices from the plate back into the soup. Remove the parmesan rind and serve warm.