Heat the oven to 425°F and line a sheet pan with parchment paper.
Soak the potatoes in cold water 15 minutes, drain, and pat completely dry.
Toss with oil, cornstarch and salt, spread in a single layer, and bake 35 to 40 minutes, flipping once, until deep golden and crisp.
While the fries bake, melt the butter in a small saucepan over medium heat and whisk in the flour, cooking 1 minute until it smells nutty and no raw flour lumps remain.
Whisk in the beef broth gradually, then add the Worcestershire sauce and black pepper.
Simmer the gravy 5 to 6 minutes, whisking often, until it coats the back of a spoon and leaves a clean line when you drag a finger through it.
Pile the hot fries onto a shallow serving dish and scatter the cheese curds over them while the fries are still hot.
Pour the hot gravy over the top just before serving so it starts to soften the curds right as guests dig in.
Finish with chopped chives.
Good to Know
Make the gravy up to 3 days ahead and reheat it gently with a splash of broth, whisking out any skin that forms on top.