Preheat the oven to 350 F / 180 C. You're going to bake the sausage and the potatoes at the same time, but in different pans.
Line a baking sheet with parchment paper or spray with non-stick cooking spray. Add the whole sausages to the baking pan and set aside. You'll be baking the sausage alongside the potatoes in the next step.
In a separate 9x13-inch casserole dish, add the diced potatoes. Sprinkle with salt and pepper, mix the canned soup with milk and pour on top, and give it a gentle toss with a wooden spoon.
Bake the sausages and the potatoes (in separate dishes) in the oven for 20 minutes. Set aside.
Remove the sausages from the baking dish. With the help of tongs and a sharp knife, cut the sausages into ½ inch bite-sized pieces.
Add the sausage to the casserole dish with the creamy potatoes and stir with the wooden spoon.
Bake this combined dish of sausage and potatoes for 20 minutes.
Add cheese on top, then cook for a final 20 minutes until the cheese melts. (Optionally, you can sprinkle paprika on top to make the cheese extra golden brown.) You can also broil for a minute or two to brown the top.
Remove, allow to rest for 5 minutes. Garnish with parsley and serve.