Melt 2 tablespoons butter in a saucepan over medium heat
Add 2 tablespoons all-purpose flour and whisk for 1 minute
Slowly whisk in 2 cups chicken broth until smooth
Add 1 cup milk or half-and-half and whisk until combined
Stir in 1 cup cooked shredded chicken
Add salt and black pepper to taste
Simmer for 5 to 10 minutes, stirring often, until thickened
Remove from heat and use as desired