Stir the cornstarch and water together in a small bowl until no dry patches remain, then set it aside. The mixture should look smooth and loose, with no white lumps settled at the bottom.

Melt the butter in a large saucepan, add the flour, and stir regularly for about 5 minutes. The roux is ready when it turns golden brown and gives off a warm, nutty aroma.

Whisk in the beef broth and chicken broth, bring the gravy to a boil, then stir in about half of the cornstarch mixture and simmer for about 1 minute. Add more slurry in small additions only if needed, then season with pepper and salt to taste when the gravy lightly coats a spoon.

Cut the potatoes into 1/2-inch sticks, cover them completely with cold water in a large bowl, and soak for at least 1 hour. The water will turn cloudy as surface starch washes away from the cut potatoes.

Heat frying oil in a deep fryer or large, wide, heavy pot to 300°F, then drain the potatoes and blot them very dry with paper towels. Dry potatoes should feel matte rather than wet, which helps them fry instead of steam.

Fry the potatoes at 300°F for 5 to 8 minutes, then transfer them to a wire rack and raise the oil temperature to 375°F. After the first fry, the potatoes should be tender and pale with little to no browning.

Return the potatoes to the 375°F oil and fry until golden brown, then move them to a paper towel-lined bowl. The finished fries should look deeply golden and feel crisp at the edges.

Place the hot fries in a large clean bowl, season lightly with salt, and use tongs to toss them with hot gravy until mostly coated. The fries should glisten with gravy while their edges still hold their shape.

Add the cheese curds, toss once more with the hot fries and gravy, then finish with freshly ground pepper and serve immediately. The curds should soften slightly and stay distinct rather than melt into a smooth sauce.