In a large pot, melt butter over medium-high heat. Add diced onion, celery, and chopped broccoli. Cook until softened, about 3-5 minutes. Sprinkle with flour and cook for an additional minute, stirring constantly.

Slowly add chicken broth, heavy cream, milk, crushed red pepper flakes, salt, and black pepper. Use a whisk to combine. Stir in the diced cooked chicken. Heat over medium heat until warm, about 10-15 minutes.

To make pie crust dippers: Preheat oven to 450°F (230°C). Unroll thawed pie crust onto a parchment paper-lined baking sheet. Cut into strips and bake for 6-8 minutes, or until golden brown. Remove from oven.

To serve, ladle soup into individual bowls. Top with shredded cheddar cheese and pieces of pie crust dippers, if desired. Enjoy!