Place the chicken breasts, diced carrots, diced celery, diced onion, and minced garlic into the crock pot.
Pour the chicken broth over the ingredients in the crock pot.
Add dried thyme, dried parsley, salt, black pepper, and paprika to the crock pot and stir gently to combine.
Cover and cook on low for 6 hours, or until the chicken is cooked through and vegetables are tender.
Remove the chicken breasts from the crock pot and shred them using two forks.
In a medium saucepan, melt the butter over medium heat.
Whisk in the flour and cook for 2 minutes, stirring constantly, to create a roux.
Gradually whisk in the whole milk and heavy cream until smooth and thickened, about 3-5 minutes.
Add the shredded chicken back into the crock pot along with the frozen peas and corn.
Pour the milk and cream mixture into the crock pot and stir well to combine.
Cover and cook on high for an additional 15 minutes to heat through and thicken the soup.
Preheat the oven to 400°F (200°C).
Roll out the refrigerated pie crust on a lightly floured surface and cut into small squares or strips for topping.
Place the pie crust pieces on a parchment-lined baking sheet and brush with beaten egg.
Bake in the preheated oven for 10-12 minutes or until golden brown and crispy.
Serve the soup hot, topped with the baked pie crust pieces as a crunchy garnish.