Sweat the onions, carrots and celery together with a tiny bit of canola oil; cook for 5 minutes until translucent.
Meanwhile, pick meat off of rib bones; chop into small pieces. I know this is a PIA, but trust me – it is worth it. You can save the bones for your next veal stock exercise. If not – freeze them anyway, because we will do it here one day!
Remove fat from prime rib; cut the remaining meat into small dice. You can do what you like with the fat – I like to rub it on my face for those creamy looking cheeks. (I am not serious! Give it to your dog if you like.).
Add meat to the pan; sweat for a minute or two to warm through.
Add red wine; reduce to 1/10th. Do this gently or risk toughening the meat. That would not be nice, would it?.
Add jus, reduce until the mixture thickens and coats the prime rib like a gravy. If you do not already love the smells of this dish, go to the doctor now, because something is wrong with you.
Combine potatoes together, careful not to completely combine the two. You would like to have some interest in the dish, no? Marbled looks better than orange. It might even be a conversation piece. Sure.
Adjust the seasoning of the potatoes and meat mixture with salt and pepper. No going back now, so get it right. Does it need more salt? Pepper?.
Ladle the mixture into your serving dishes. You can either go big or you can go individual.
Cover the meat/gravy mixture with the combined mashed potatoes; smooth to cover the meat.
Score the top with a fork; brush with melted butter. Don’t do it so hard you wreck your rows. Trust me, that sucks.
Sprinkle paprika on top of potatoes.I said sprinkle, avoid clumps. One way is with a small strainer.
Bake in 175 °C (350 °F) oven for 35-40 minutes or until the top is browned and the meat mixture is threatening to bubble through.