Melt butter in a heavy saucepan over low heat. Add 3 Tbsp. flour, stirring until smooth. Cook 1 minute, stirring constantly.
Gradually add 1/2 cup milk; cook over medium heat, stirring constantly, until mixture leaves sides of pan. Stir in salt and pepper. Remove from heat; stir in mayonnaise and chicken. Cover and chill 1 hour.
Shape chicken mixture into 6 balls or logs. Combine egg and 1 Tbsp. milk, mixing well. Dredge croquettes in flour, dip in egg mixture, and roll in cracker crumbs.
Deep-fry, a few at a time, in hot oil (370 degrees) for 3 to 5 minutes, or until golden brown. Drain on paper towels.
Ingredients:
3 tb Butter
3 tb Flour, plus extra for dredging
1/2 c Plus 1 Tbsp. milk
1/4 ts Salt
1/4 ts Pepper
1/2 c Mayonnaise
2 c Minced cooked chicken
1 Egg, beaten
1 c Finely crushed saltine
Cracker
Crumbs