Chicken Pot Pie Soup

Name: Chicken Pot Pie Soup
Ingredients: 1 refrigerated pie dough; Egg wash; 1/4 c. freshly grated Parmesan; 2 tbsp. butter; 1 onion, chopped; 2 carrots, peeled and chopped into 1/2 coins; 2 stalks celery, chopped; 2 cloves garlic, minced; 2 tbsp. all-purpose flour; 1 c. water; 4 c. low-sodium chicken broth; 1 c. whole milk; 4 medium Yukon gold potatoes, chopped; Kosher salt; Freshly ground black pepper; 1/2 tsp. sweet paprika; 1 c. corn; 1 c. chopped green beans; 1 1/2 c. frozen peas, defrosted; 1 1/2 c. shredded rotisserie chicken; 2 tbsp. chopped fresh parsley