Place flour in a heavy saucepan, gradually blend in milk with a wire whip. Stir over moderate heat until mixture begins to lump. Remove from heat and vigorously blend in egg yolks. When smooth, beat over heat 2 minutes to thicken sauce. Remove from heat; beat in seasonings and butter. When sauce is slightly cool, add flavoring. Spread ½ inch thick in a lightly buttered platter. Film surface with melted butter; cover and chill several hours.
Turn the flour in one plate, beaten egg in second, and crumbs in third. Scoop up 1½ tablespoons chilled mixture with a spatula; drop into flour. Dredge lightly and shape into a square with fingers. Drop into egg and spoon it over entire surface. Drain on a fork and drop into crumbs. Pat crumbs evenly over entire surface. (*) Croquettes may be crumbed a day in advance; cover and refrigerate.
Brown 4 to 5 croquettes at a time for 2 to 3 minutes in frying oil at 375 degrees. Drain on crumpled paper towels. Reheat if necessary for 2 to 3 minutes only in a preheated 450-degree oven.