In a large saucepan, heat the butter over medium-high heat. Add the onion and celery and cook, stirring often, until softened but not brown, 6 to 7 minutes. Stir in the flour until incorporated, about 30 seconds. Add the chicken broth and cook for 1 minute. Stir in the milk and bring to a boil. Lower the heat, cover the pot and simmer until slightly thickened, about 5 minutes.