Prepare the piperade: Peel the peppers, seed and cut them into fine dice (brunoise), along with the tomato and Anglet pepper. Quickly blanch, then sweat in a little olive oil. Set aside.
Prep the tomatoes: Remove the tops, hollow them out, salt the insides, and place upside down on a rack to drain well.
Poach the eggs: Bring water to a boil in a saucepan with a splash of vinegar. Crack eggs into 6 ramekins, then gently slide into simmering water, 3 at a time. Cook 3 minutes, remove with a slotted spoon, and drain on paper towels. Repeat for remaining eggs.
Make the sauce: Mix ketchup with fresh cream, salt, pepper, and Anglet pepper.
Assemble: Place drained tomatoes right-side up on a platter. Fill each halfway with piperade, top with a cooled poached egg, wrap with Bayonne ham, and drizzle with sauce. Scatter remaining piperade around the tomatoes.
