Heat olive oil in a large pot over medium heat. Add onion, garlic, carrots, and celery. Sauté for 5 minutes until softened.
Sprinkle flour over the vegetables and stir well. Cook for 1-2 minutes to remove the raw flour taste.
Slowly pour in chicken broth while stirring to avoid lumps. Add milk, thyme, parsley, salt, and pepper. Bring to a gentle simmer.
Add cooked chicken, peas, and corn. Simmer for 10-15 minutes until the soup thickens slightly.
Bake puff pastry or pie crust separately until golden. Cut into pieces and serve on top of the soup for a pot pie feel.
Ladle into bowls and garnish with fresh parsley. Enjoy hot!