In three individual bowls, separately place the flour, beaten egg, and breadcrumbs.
Slice each ball of mozzarella cheese into four 1/3- to 1/2-inch thick rounds. Coat the sliced cheese in the flour, then the beaten eggs, and then the breadcrumbs.
Place on a baking sheet; cover and refrigerate until cold, at least 2 hours.
In a small frying pan over low heat, melt butter. Add garlic and saute approximately 3 minutes.
Transfer garlic/butter mixture to a food processor. Add parsley leaves, 1/4 cup olive oil, capers, anchovies, and lemon juice. Blend until a coarse paste forms. Season with salt and pepper to taste.
When ready to serve: In a large frying pan over high heat, heat the remaining 1/4 cup olive oil. Working in batches, fry prepared cheese slices until brown, approximately 2 minutes per side.
Transfer fried cheese to individual serving plates. Spoon warm anchovy sauce over the top of the cheese.
NOTE: The Mozzarella cheese and the Anchovy Sauce can be prepared 1 day ahead. Cover separately and refrigerate. Re-warm sauce slightly over low heat before serving.
* Learn how to Make Homemade Bread Crumbs.
** Anchovy Paste may be substituted for the anchovy fillets. 1/2 teaspoon anchovy paste is equal to 2 anchovy fillets. You can also adjust the amount of anchovies used according to your taste. To purchase Anchovies and Anchovy Paste, check out What's Cooking America's Kitchen Store.
Fried Mozzarella Cheese with Anchovy Sauce Recipe: https://whatscookingamerica.net/Appetizers/FriedMozzarellaAnchovies.htm