Prepare a bowl with ice and water. Line a sheet pan with paper towels.
In a 5-quart pot, bring 6 cups water to a boil over moderately-high heat. After the water has reached a boil, turn off the heat. Crack each egg into a ramekin and quickly add to the water. Once you have added all the eggs, cover the pot and set aside for 3 minutes.
Using a slotted spoon, very carefully lift the eggs out of the water and directly into the bowl of ice water to stop the cooking. Remove from the ice water and place on the prepared sheet pan.
Spread the flour on a plate and put the beaten eggs in a shallow bowl. In another shallow bowl, stir the panko with salt and pepper.
Carefully dust 1 poached egg in the flour, dusting off any excess. Transfer the poached egg to the beaten eggs, and then transfer with a slotted spoon to the panko. Coat with the panko and carefully place on a plate. Repeat with the remaining eggs.
Heat the oil in a heavy saucepan over high heat until a candy thermometer registers 350 degrees F. Using a slotted spoon, place 1 panko-coated egg into the oil and fry until golden brown, 10 to 15 seconds. Transfer the fried egg to paper towels to drain. Repeat with the remaining eggs.
Season the tomato with salt and pepper. Place 1 tomato slice on each plate and top each slice with an egg.
BYOC: Try this in early spring over some steamed asparagus. You can always add some fresh spinach to this for a crunch. Add the whole thing over a nice thick piece of crusty bread or English muffin for a fun brunch item.