plus extra for dredging
plus 1 tbsp
Melt butter in a heavy saucepan over low heat; add 3 tablespoon flour, stirring until smooth.
Cook 1 minute, stirring constantly. Gradually add ½ 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 tablespoon 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.