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. They won't seem very cup-like yet, but the flatten out a bit when cooking.
Place them facing down on a baking sheet, and place under the grill / broiler for about 5 minutes, until they are charred.
You can then 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
Put the eggs on to poach and grill the tops of the peppers if you would like to to crisp them up.
Assemble! Place the pepper on a plate and top with the poached egg and smoky mayo. Grind on some black pepper and you're good to go.