Prepare the stuffing for the peppers by mixing together the cornmeal, cheese and water in a small bowl.
Prepare the smoky mayo topping by mixing the smoked paprika into the mayonnaise.
Prepare your pepper by slicing off the top, and then cutting vertically into 2 pieces. Place them facing down on a baking sheet, and place under the grill / broiler for about 5 minutes, until they are charred.
Turn them over and stuff with the polenta mixture. Push them together on the pan to avoid the mixture spilling out onto the baking sheet.
Bake for 15 minutes at 200C / 390F.
Poach the eggs and place them on the top of the pepper cups, with a dollop of smoky mayo on top.