Put the shrimp meat and the water chestnuts into a food processor or blender, and process into a lumpy paste.
Scrape contents into a bowl and add the egg and the flour. Stir well.
Press down on the pieces of bread to flatten them. With a knife, coat each piece of bread with a mound of the shrimp mixture about an inch high. Top with a sparse sprinkling of sesame seeds. Cut each of these into quarters.
Deep-fry in vegetable oil at 325 degrees until golden brown. Drain excess oil and allow to cool for one minute.
