Cut the peppers in half lengthways and remove the seeds. Transfer to a baking dish. Bake for 20 minutes, to soften.
Cook the potato in boiling water for 7 minutes then leave to cool slightly and cut into matchsticks.
Warm the olive oil to a large frying pan set over a medium heat. Add the onions and cook about 5 minutes to soften. Add the potato and cook for a further 10 minutes, stirring constantly, until golden and cooked through. Remove from the pan and set aside. Add the sausage and cook until browned then stir in the beans and the potato and onion mix - cooking for 1-2 minutes until the beans are warm. Remove from the heat.
Spoon the sausage mixture evenly into each pepper. Divide the cheddar between them and place into the oven for 20 minutes. Remove from the oven and make a well in 4 of the halves and then add an egg into each well. Season well with salt and pepper and bake for a further 5 minutes until the egg is cooked through and the cheese melted. Served sprinkled with chives.