For the Gravy: Melt butter in a medium saucepan over medium-high heat until foaming. Whisk in flour and cook, stirring constantly, until golden blonde, about 2 minutes. In a steady stream, gradually whisk in stock. Bring to a boil, reduce to a simmer, and cook until reduced to 2 cups, 10 to 15 minutes. Remove from heat, stir in vinegar, and season with salt.

For the Fries: Place potatoes in a large bowl and cover completely with cold water. Let soak for at least 1 hour, or, alternatively, drain water and rinse again, changing water until it runs completely clear. Drain potatoes and dry thoroughly with paper towels.

Heat oil in a large Dutch oven or wok to 350°F (177°C). Working in batches, add potatoes and cook, stirring and turning frequently until pale blonde, about 5 minutes. Transfer potatoes to a paper towel-lined baking sheet. (For crispiest fries, see note about adding a freezing step.)

Heat oil to 425°F (218°C). Add potatoes and cook, stirring and turning frequently, until deep golden brown, about 3 minutes. Transfer to paper towel-lined bowl and season with salt to taste.

Reheat gravy over high heat until hot. Place fries in a shallow bowl or dish, top generously with cheese curds, and ladle on gravy. Sprinkle with minced chives (optional). Serve immediately.