Step 1
Preheat the oven to 170°C/325°F/Gas Mark 3. Soak the bread in water for 1 minute, then squeeze dry and finely chop. Tip into a bowl and add the onion, carrot, celery, parsley, Parmesan, egg and thyme. Season to taste and mix well to combine.
Step 2
Cover the steak slices with clingfilm and flatten out with a steak hammer or rolling pin to a 3 mm thickness. Place a piece of Parma ham on top of each slice of beef, trimming them down as necessary and then spread the stuffing on top. Roll each one in a Swiss roll shape and secure with toothpicks.
Step 3
Heat a heavy-based casserole dish that has a lid. Add the oil and quickly sear the beef rolls on all sides until lightly golden – you may have to do this in batches depending on the size of your dish.
Step 4
Arrange all the beef rolls in the casserole dish and pour in the wine. Add 50 ml of water, then cover and cook in the oven for 1½ hours or until the beef rolls are completely tender, adding a little more water if at any time it looks like the beef is going to cook dry.
Step 5
Meanwhile, preheat a separate oven to 200°C/400°F/Gas Mark 6 to make the gratin. Cook the potatoes in a pan of boiling salted water for 15-20 minutes until tender. Drain well and return to the pan, then roughly crush with a fork. Tip into a baking dish. Mix together the Parmesan and parsley and sprinkle over the potatoes, then drizzle the olive oil on top. Roast for 8-10 minutes or until bubbling and lightly golden.
Step 6
Arrange the stuffed braised beef on warmed plates, spoon over a little of the remaining juices and serve with a generous helping of the crushed new potato and Parmesan gratin.