1. Place one slice of bread on working surface, then place 2 slices of prosciutto and 2 slices of mozzarella on top of bread and then place another slice of bread on top.
2. Trim the crusts, cut in half forming 2 rectangles and place 2 toothpicks through each of the rectangular sandwiches to hold together.
3. Repeat using other 2 slices of bread, mozzarella, and prosciuto.
4. Dredge each spedini in flour then dip in egg, covering all sides.
5. Heat remaining 1/4 cup of olive oil in large saute pan over medium heat.
6. Heat about 3 inches of vegetable oil in a large saute pan over high heat.
7. Place spedini in pan and fry on both sides until brown.
8. Place spedini in serving plates and remove the toothpicks.
9. Melt 2 tablespoons of butter in a sauté pan over medium heat.
10.Add anchovy filets and sautee until anchovies are heated through.
11.Pour anchovy sauce over spedini and serve.