Preheat the oven to 200°C/400°F/Gas mark 6.
Combine the potatoes, two tablespoons of oil and a good pinch of salt and pepper in a large bowl, and toss to coat the potatoes.
Spread the chips evenly on a large baking sheet and roast in the oven, stirring once or twice, for 20–25 minutes, until the potatoes are tender and browned.
Whisk 115ml of beef stock and the flour in a small bowl, then set aside.
Heat the remaining three tablespoons of oil in a medium saucepan over a medium heat. Add the mushrooms and onion and cook, stirring often, for 5–7 minutes, until beginning to brown. Add the remaining beef stock and bring to a simmer. Cook for 8–10 minutes, until reduced by about half.
Add the reserved flour and stock mixture and continue to cook, stirring constantly, until the gravy is smooth and thickened. Stir in the chives and season with sea salt and pepper. Set the gravy aside and keep warm until needed.
When the potatoes are done, push them together in the centre of the baking sheet and sprinkle with the cheese. Return to the oven and bake for approximately 5 minutes more, until the cheese is melted.
Serve the potatoes topped with the gravy.