Cook mince, on medium / high heat, in a wide based pan until lump free and brown.
Add onion, celery, apple and pepper and cook for a further 2 mins.
Add 1/2 cup of stock and stir. Cover and simmer for approx 45 mins, stirring occasionally making sure that the mince does not dry out.
Add a further 1/2 cup of stock and repeat simmering process.
Add a further 1/2 cup of stock and simmer for 30 mins with lid on and then remove lid for 15 mins.
Towards the end of cooking the mince, add the carrots and potato to a large pan and cover with water. Bring to the boil, cover and simmer until tender (approx 20 mins)
Drain the carrots/potatoes and mash.
Melt the butter and milk together and add to the carrots / potatoes and mash until smooth.
Transfer the mince to a oven proof dish (mine was a 1/2 litre capacity)
Top with the potato / carrot mash.
Beat the egg and brush the top of the mash
Bake in oven (180C / 350F) for 25 mins.