Melt the butter in a saucepan over medium heat. Add the 5 tablespoons flour and stir to create a paste. Cook gently to remove the raw flour taste, stirring constantly, about 2 minutes. Add the milk, little by little, stirring constantly with a whisk so as to avoid lumps. Using a rasp, grate the garlic into the sauce and season with the nutmeg and cayenne. Cook, stirring frequently, about 20 minutes.
Remove from the heat and crumble the cheese into the sauce, stirring to incorporate. Scrape the mixture into an oiled baking dish and cover with plastic wrap, gently pressing the wrap against the surface to avoid a skin. Chill until set, 4 to 5 hours.
Heat several inches of oil in a large pot to 350 degrees F.
Place the remaining 1 cup flour and the breadcrumbs in separate shallow dishes. Beat the eggs in a third shallow dish. Using a spoon, scoop 1/2-ounce portions of the cheese mixture. Coat in the flour, shape into small balls, dip in the egg wash and coat with the breadcrumbs.
Carefully add the croquettes to the hot oil and fry until golden brown. Serve with Pickled Apples.
Bring the vinegar, sugar, 1 cup water and salt to a simmer. Let cool. Slice the apples 1/2-inch thick, to desired shape. Pour the cooled pickling liquid overtop. Refrigerate up to 1 week.
Recipe courtesy of Executive Chef Michael Anthony, Gramercy Tavern, NYC