Heat the butter in a large stock pot over medium-low heat. Add in the onion, carrots, celery and garlic with a big pinch of salt and pepper - I’d say at least ½ teaspoon salt and pepper to start. Cook, stirring occasionally, until the vegetables soften. Stir in the garlic cloves and italian seasoning. Stir in the shredded chicken.
Add in 5 cups of chicken stock and the parmesan rind. Bring the mixture to a boil, then reduce it to a simmer. Stir in the pearl couscous. Cook uncovered, stirring occasionally, until the couscous is done, about 10 to 12 minutes.
Fill a shaker cup with the milk. Add the flour to the milk and shake the cup for at least 30 seconds. Stream in the milk slurry while stirring. Bring the soup back to a simmer and let it simmer for 5 or 10 more minutes as it thickens.
Add in the lemon juice and fresh parsley. Taste the soup and if it needs more salt and pepper, add it (it will need it!). If the parmesan rind didn’t melt entirely, you can scoop it out at this point. You can also decide if you’d like to add the additional cup of chicken stock here - it depends on how hearty or how brothy you like your soup. The couscous will soak it up as it sits!
Serve immediately with a lemon wedge for sprinkling, parmesan cheese for topping and parsley sprinkled on top.